Categories
Device

How to learn about compound interest and investing using the one‐penny trick

You may have read or heard that Albert Einstein said, “The power of compound interest the most powerful force in the universe.” Whether this is true or simply an important quote attributed to a great mind to give it more weight, compound interest is indeed remarkable, and you should use it to your advantage whenever possible.

When it comes to managing your money, generally the more risk you’re willing to accept, the higher your potential returns. Historically, over the long term, putting money into stocks gives you a lot more return on your investment than putting it into a savings account (or stuffing it under the mattress).

After the recession that began in 2008, many people became risk-averse, and some decided to settle for lower returns in order to decrease risk. The problem is, putting all your money in an ordinary savings account may keep it safe, but the returns may not even keep up with inflation. While you should have a savings account for emergencies, putting some of your money in higher-risk investments has the potential for helping your long term financial prospects much more.

Compounded Interest

Here is a simple formula for calculating returns based on a flat interest rate that’s compounded once per year:

Total return = Initial investment × (1 + i)^n

Where i = the interest rate and n = the number of years the money is invested

While this formula greatly oversimplifies compounding, since interest rates fluctuate and many savings vehicles compound more often than once per year, it can show how powerful compounding is. The interest rate is the key to how much your initial investment grows, as you can see from the following chart showing an initial investment of $1,200:

*historical rate of return. This is, of course, not guaranteed.

Learn more: Sign up for Mint and learn about our great budgeting and investment tools.

As you can see, putting money into an ordinary savings account probably won’t even let you outpace inflation, and that’s before bank fees are taken into account. Compounding is great, but it’s even greater when you “goose” it by adding to your savings every year.

Add Another $1,200 Each Year and Compounding Is More Impressive

Putting $1,200 in a savings account and forgetting about it for 40 years may keep it safe, but who knows how much $1,465 will be worth after that many years? Suppose that every year you save up $100 per month and then add that $1,200 to your savings. Results are pretty impressive:

Get Sound Financial Advice and Diversify

This is not to say you should put every spare dime into stocks, or just throw extra money at the stock market without doing your homework first. People have lost fortunes in the stock market, sometimes due to short-sighted investing, and sometimes due to factors beyond their control. This exercise is simply to show you that compounding is your friend when it comes to making money, and that if you’re willing to accept higher risks, you may have substantially higher returns.

If you want to start investing, get your day-to-day finances in order first. Create a budget using great online tools like Mint, get three to six months’ worth of living expenses in a savings account for emergencies, max out your IRA or 401K contributions, and generally make sure you and your family are on sound financial footing.

Don’t start investing without learning about your choices beforehand. Many community classes offer basic courses in investing that can be well worth your time. Working with a certified financial planner is not just for the wealthy, but can be a very smart move for the middle class investor too. Just make sure to do your research first and choose carefully.

Once you start investing, you can use tools like Mint to help you track your investments. You can also learn more about your personal investment style, and use Mint to expose fees hidden on financial statements and in the fine print that reduce the long-term growth of your investments. Educate yourself, enlist in the advice of investing experts, and use Mint to track your budget and investments, and you set yourself up for the brightest financial future.

Learn more: Sign up for Mint and learn about our great budgeting and investment tools.

Options Trading from Scratch

Learn everything you need to know about successful options trading with this three-part video course.

Market Data and Calendars

Looking for new stock ideas? Want to see which stocks are moving? View our full suite of financial calendars and market data tables, all for free.

Investing Education and Resources

Receive a free world-class investing education from MarketBeat. Learn about financial terms, types of investments, trading strategies and more.

MarketBeat empowers individual investors to make better trading decisions by providing real-time financial data and objective market analysis. Whether you’re looking for analyst ratings, corporate buybacks, dividends, earnings, economic reports, financials, insider trades, IPOs, SEC filings or stock splits, MarketBeat has the objective information you need to analyze any stock. Learn more.

© American Consumer News, LLC dba MarketBeat® 2010-2020. All rights reserved.
326 E 8th St #105, Sioux Falls, SD 57103 | [email protected] | (844) 978-6257
MarketBeat does not provide financial advice and does not issue recommendations or offers to buy stock or sell any security. Learn more.

© 2020 Market data provided is at least 10-minutes delayed and hosted by Barchart Solutions. Fundamental company data provided by Morningstar and Zacks Investment Research. Information is provided ‘as-is’ and solely for informational purposes, not for trading purposes or advice, and is delayed. To see all exchange delays and terms of use please see disclaimer.

Nov 7, 2019 1:02 PM EST

The Street Illustration

Compound interest is one of the most useful and helpful tools when it comes to saving money. Whether a person is saving money for their rainy day or emergency fund or taking the next step to set aside a portion of their paycheck for longer-term goals like their retirement, the accumulation of interest boosts that goal.

Saving as much money as you can and doing so when you are younger makes it more effective. This basic concept means that a person earns interest on top of the interest whether they have $500 or $5,000 saved.

Many experts have touted compound interest as the greatest advantage that investors have to accumulating more money for a down payment for your first house, vacations or retirement. Forgoing that dessert or expensive pair of earbuds really does add up in the long run.

What Is Compound Interest?

Compound interest is pretty simple – it’s when the money you have saved earns interest from a bank or credit union or retirement account like a 401(k) plan or IRA. It also works in reverse. The interest you accumulate from not paying off the balance of your credit card account or a high-interest personal loan can add up quickly, making it more difficult to save money.

In layman’s terms, compound interest is simply interest on interest. The more money you are able to sock away in a savings account, CD or retirement account, the more interest you can earn. Even if you are only able to save a small amount such as $25 a week or $100 a month, the compound interest on that amount can accumulate quickly.

How to Calculate Compound Interest

The formula for calculating how much compound interest will result in your principal amount becoming is:

A = P (1 + r/n)(nt)

In this equation, P is the principal, r is the interest rate, n is the amount of compounding periods in a year and t is the amount of time in years. Using this equation we can calculate A, aka the final amount.

So let’s use an example. You deposit $15,000 into a savings account that has a 5% interest rate compounded monthly for 10 years. This would make r .05 and n 12. If we input everything into the formula, it would be:

A = 15,000(1 + 0.05/12)(12*10) = 15,000(1 + 0.0041667)(120) = 15,000(1.64700949769) = 24,705.1424654

In 15 years, your $15,000 deposit would turn into approximately $24,705.14.

If you were just trying to find out how much interest it would be without the principal amount, simply do the formula and then subtract the principal amount. That would give us 24,705.142654 – 15,000 = 9,705.14246535. That would be about $9,705.14 in interest.

How Compound Interest Impacts Savings Accounts

Many individuals start saving money and earning interest in a basic savings account since there no penalties for withdrawing money. Consumers can increase the amount of money they have saved and earn more interest when they automatically have money allocated from their paycheck into a savings account.

When an individual does not take money out of their savings account, he/she can earn more interest. Simple interest is interest on principal only. If a person puts $100 in a savings account and earns 10% interest annually, the account will be worth $110 in one year. If that money stays invested earning 10% interest for one more year, there will be $121 in the account – $10 simple interest each year and $1 interest for the second year on the $10 earned in interest the first year. Adding more money in the second year will yield more savings because it will be added to the new balance.

How Compound Interest Helps Grow Retirement Accounts

The sooner employees are able to start saving money in a 401(k) plan, IRA or Roth IRA, the more money they can accumulate because of compound interest. Investing in stocks through a mutual fund or ETF can increase the amount of money in a retirement portfolio. Experts recommend that investors start saving for retirement even if the amounts are smaller in the beginning such as $200 a month and have a diversified portfolio of stocks. As your salary rises each year, increase the amount you are saving for your retirement. Avoid spending bonuses and try to save those amount also for your retirement.

Watching the fees charged by a mutual fund, retirement plan or financial adviser is also important because the fees also compound over time similar to investment returns. Even a 1% fee that appears innocuous adds up over 30 or 40 years.

For instance, a person who socks away money from their paycheck into a retirement account that grows by 8% annually before fees and pays 1% of assets under management to have that account managed is really earning 7% compounded annually. If the account had saved $1 million then in 20 years, the amount would grow to $3.87 million. However, if the person did not have to pay 1% each year in fees, then the individual would have accumulated $4.66 million for retirement. While 1% does not sound like a lot of money, in this scenario, it means losing out on $790,000.

Many experts, such as college professors and financial advisers recommend that people start saving as soon as possible. The longer you save money, the more money you can earn from just interest.

Even during volatile periods in the stock market, the longer a person accumulates money in a retirement account, the more money is accumulated.

When Compound Interest Hurts Consumers

On the flip side, accruing too much interest is detrimental to an individual. The interest calculated by credit cards companies, pay day lenders or other lenders which provide auto loans or mortgages can accumulate quickly.

Consumers who are only making minimum payments for their monthly credit card payments are often only paying interest because a small portion of their payment goes toward the principle amount or the amount of money borrowed.

Since many credit card companies are charging interest rates that are double digits, paying more than the minimum amount will decrease the amount owed much faster. When you increase a monthly payment by an additional $50 or $100, it means that more money is paid each month toward the original amount of money that was borrowed and less on the interest.

As interest rates continue to rise because of the decisions made by the Federal Reserve, people who continue to carry a balance on their credit cards will wind up paying more money in interest. Since the interest rates for credit cards are adjustable, meaning they can increase at any time, when the Fed raises the federal funds rate, they also rise. If you have high interest rates from your credit card company or another loan, making extra payments will help lower the balance sooner. Refinancing a loan or mortgage is also an option and helps lower the amount of interest you are paying each month.

Once you pay off the credit card payment, you can start taking that same $200 you paid each month for the bill and allocate it into a CD or money market account to save for emergencies so you can avoid paying high interest rates.

Compound interest is one of the most powerful forces of investing. Here’s how to calculate it.

When it comes to calculating interest, there are two basic choices: simple and compound. Simple interest simply means a set percentage of the principal every year, and is rarely used in practice.

On the other hand, compound interest is applied to both loans and deposit accounts. Compound interest essentially means “interest on the interest” and is the reason many investors are so successful.

Comparing simple and compound interest
Let’s say you invest $10,000 at 8% simple interest. This means that after the first year, $800 is added to your account. In the second year, another $800 in interest is paid, and the same with the third year, fourth year, and so on.

If your investment paid 8% compound interest on an annual basis, it wouldn’t make a difference at first. After the first year, you’d receive the same $800 interest payment as you would with a simple interest calculation. However, this is where it starts to get very different.

In the second year, your 8% interest is calculated on your entire new balance of $10,800, not just your original $10,000. This produces an interest payment of $864 for the second year, which is then tacked on to the principal when calculating your interest for the third year.

You may be surprised at how quickly this can add up. At 8% simple interest, your $10,000 investment would be worth $34,000 after 30 years. However, using compound interest, the value would balloon to more than $100,000. Just take a look at how simple and compound interest compare over a 50-year period:

How to Learn About Compound Interest and Investing Using the One‐Penny Trick

Compounding frequency makes a difference
In the previous example, we used annual compounding — meaning that interest is calculated once per year. In practice, compound interest is often calculated more frequently. Common compounding intervals are quarterly, monthly, and daily, but there are many other possible intervals that can be used.

The compounding frequency makes a difference — specifically, more frequent compounding leads to faster growth. For example, here is the growth of $10,000 at 8% interest compounded at several different frequencies:

Once you learn about the magic of compounding, it’s natural to want to put its power to work building your wealth.

How to Learn About Compound Interest and Investing Using the One‐Penny Trick
Small sums can grow into large sums through compounding. Photo: Damian Gadal, Flickr

This article was originally published on Sept. 4, 2015. It was updated on April 5, 2016.

Once you learn about the magic of compounding, it’s natural to want to put its power to work building your wealth. You might then wonder what kind of investment accounts earn compound interest. Let’s review compounding itself, along with interest, and then tackle the different kinds of accounts you might consider.

What is interest?
Compounding is often referred to in relation to interest. Interest is essentially a reward for lending money. Banks charge interest when they lend money for mortgages or car loans, and credit card companies charge it, too, when you carry a balance of debt on your card. You can collect interest if you have money in certain bank accounts or other accounts. That’s because the money you have in your bank account is available for the bank to use, such as when it lends money to other customers. Thus, it rewards you for leaving your money with it.

Interest comes in two primary varieties: simple and compound. If you have $1,000 in an account that pays you 3% simple interest annually, you’ll collect $30 each year. If the interest is compound, then you will get $30 in your first year, and if you have $1,030 in your account the next year, you’ll collect 3% of that, or $30.90. That’s compounding doing its thing.

What is compounding?
Compounding is happening when your investment grows each year — and when the amount it grows by also grows. In other words, your investment generates earnings, and then those earnings generate earnings of their own. It’s a relatively simple concept, but with mind-blowing possibilities, as the longer you let your investment grow, the more rapidly it will grow. Check out this example of a single $1,000 investment growing at 10% annually:

Gain in Previous 5 Years

See? Over the first five years, your modest investment grows by $611. But decades later, it’s growing by tens of thousands of dollars every five years. And that’s just with a single $1,000 investment. Imagine what happens if you start with $5,000 or $10,000 and if you add more money to your account regularly.

So where can you take advantage of this kind of growth?

How to Learn About Compound Interest and Investing Using the One‐Penny Trick

Many bank accounts offer compounded interest, though current rates are relatively low. Photo: Mike Mozart, Flickr.

Bank accounts earn compound interest
Bank accounts are classic compounding vehicles. A key feature of most savings accounts is the interest they pay, which will typically be higher than interest you can earn on checking accounts. (Many checking accounts pay no interest at all.

You can also earn compounded interest in money market accounts and certificates of deposit (CDs).

Some bonds earn compound interest
Many bonds pay fixed interest sums, but some, such as zero coupon bonds, incorporate compounded growth. A typical bond might have you paying the face value of the bond, which might be $10,000, and then collecting regular interest payments (often referred to as coupons) before getting the face value back at maturity. With a zero coupon bond, though, even though its face value might be $10,000, you’ll pay less for it, such as, perhaps, $9,500. You’ll receive no interest payments, but at maturity, you’ll collect $10,000, not the $9,500, with the difference representing the compounded value of interest payments.

The power of compounding — in non-interest-bearing investments
It’s important to understand that the compounding is at work in scenarios other than interest, too. Think, for example, of stocks that pay dividends. If you reinvest your dividend payments into shares of more stock, then those shares will grow, too, ideally kicking out dividend payments of their own. The reinvestment can help your portfolio grow faster than it otherwise would, if you didn’t reinvest those sums.

Compounding can also help you project your portfolio’s performance, for financial-planning purposes. If you have a portfolio of $100,000 in stocks, for example, and you hope that it will grow by at least an average of 7% annually over the coming 20 years, you can run the numbers and see that you can expect to have at least $387,000 in 20 years.

It’s smart to aim for compounded growth in your portfolio. Bank accounts won’t offer you rapid growth because of the current low interest rate environment, but don’t always write them off. There have been plenty of years with interest rates in meaningful ranges and some years with double-digit interest rates, too. And remember that stocks can give you compounded growth, too.

One way to invest in stocks is through a brokerage. There are many institutions that offer online investment accounts. If you need help sorting through the options, head over to our broker tool, which lets you you compare account features and explore investment options.

Examples of Compound Interest

The following examples of compound interest formula provide an understanding of the various types of situations where the compound interest formula can be used. In case of compound interest, interest is earned not only on principal amount which is invested initially but it is also earned on the interest earned previously from the investment. There are a different number of periods for which the compounding of the interest can be done which depends on the terms and conditions of the investment like compounding can be done on a daily, monthly, quarterly, semi-annually, annually basis, etc.

We can now see some of the different types of compound interest formula examples below.

How to Learn About Compound Interest and Investing Using the One‐Penny Trick

Example #1

Case of Compounded Annually

Mr. Z makes an initial investment of $ 5,000 for a period of 3 years. Find the value of the investment after the 3 years if the investment earns the return of 10 % compounded monthly.

Solution:

In order to calculate the value of the investment after the period of 3 years annual compound interest formula will be used:

In the present case,

  • A (Future value of the investment) is to be calculated
  • P (Initial value of investment) = $ 5,000
  • r (rate of return) = 10% compounded annually
  • m (number of the times compounded annually) = 1
  • t (number of years for which investment is done) = 3 years

Now,the calculation of future value (A) can be done as follows

How to Learn About Compound Interest and Investing Using the One‐Penny Trick

  • A = $ 5,000 (1 + 0.10 / 1) 1*3
  • A = $ 5,000 (1 + 0.10) 3
  • A = $ 5,000 (1.10) 3
  • A = $ 5,000 * 1.331
  • A = $ 6,655

Thus it shows that the value of the initial investment of $ 5,000 after the period of 3 years will become $ 6,655 when the return is 10 % compounded annually.

Compound Interest Formula Example #2

Case of Compounded Monthly

Mr. X makes an initial investment of $ 10,000 for a period of 5 years. Find the value of the investment after the 5 years if the investment earns the return of 3 % compounded monthly.

How to Learn About Compound Interest and Investing Using the One‐Penny Trick

Solution:

In order to calculate the value of an investment after the period of 5 years compound interest formula monthly will be used:

In the present case,

  • A (Future Value of the investment) is to be calculated
  • P (Initial value of investment) = $ 10,000
  • r (rate of return) = 3% compounded monthly
  • m (number of the times compounded monthly) = 12
  • t (number of years for which investment is done) = 5 years

Now,the calculation of future value (A) can be done as follows

How to Learn About Compound Interest and Investing Using the One‐Penny Trick

  • A = $ 10,000 (1 + 0.03 / 12) 12*5
  • A = $ 10,000 (1 + 0.03 / 12) 60
  • A = $ 10,000 (1.0025) 60
  • A = $ 10,000 * 1.161616782
  • A = $ 11,616.17

Thus it shows that the value of the initial investment of $ 10,000 after the period of 5 years will become $ 11,616.17 when the return is 3 % compounded monthly.

Compound Interest Formula Example #3

Case of Compounded Quarterly

Fin International Ltd makes an initial investment of $ 10,000 for a period of 2 years. Find the value of the investment after the 2 years if the investment earns the return of 2 % compounded quarterly.

Solution:

In order to calculate the value of the investment after the period of 2 years compound interest formula quarterly will be used:

In the present case,

  • A (Future Value of the investment) is to be calculated
  • P (Initial value of investment) = $ 10,000
  • r (rate of return) = 2% compounded quarterly
  • m (number of the times compounded quarterly) = 4 (times a year)
  • t (number of years for which investment is done) = 2 years

Now,the calculation of future value (A) can be done as follows

How to Learn About Compound Interest and Investing Using the One‐Penny Trick

  • A = $ 10,000 (1 + 0.02 / 4) 4*2
  • A = $ 10,000 (1 + 0.02 / 4) 8
  • A = $ 10,000 (1.005) 8
  • A = $ 10,000 * 1.0407
  • A = $ 10,407.07

Thus it shows that the value of the initial investment of $ 10,000 after the period of 2 years will become $ 10,407.07 when the return is 2% compounded quarterly.

Compound Interest Formula Example #4

Calculation of rate of return using Compound Interest Formula

Mr. Y invested $ 1,000 during the year 2009. After the period of 10 years, he sold the investment for $ 1,600 in the year 2019. Calculate the return on the investment if compounded yearly.

Solution:

In order to calculate the return on an investment after the period of 10 years, the compound interest formula will be used:

In the present case,

  • A (Future Value of the investment) = $ 1,600
  • P (Initial value of investment) = $ 1,000
  • r (rate of return) = to be calculated
  • m (number of the times compounded yearly) = 1
  • t (number of years for which investment is done) = 10 years

Now, the calculation of the rate of return (r) can be done as follows

How to Learn About Compound Interest and Investing Using the One‐Penny Trick

  • $ 1,600 = $ 1,000 (1 + r / 1) 1*10
  • $ 1,600 = $ 1,000 (1 + r) 10
  • $ 1,600 / $ 1,000 = (1 + r) 10
  • (16/10) 1/10 = (1 + r)
  • 1.0481 = (1 + r)
  • 1.0481 – 1 = r
  • r = 0.0481 or 4.81%

Thus it shows that Mr.Y earned a return of 4.81 % compounded yearly with the value of the initial investment of $ 1,000 when sold after a period of 10 years.

Compound Interest Examples Video

Conclusion

It can be seen that the compound interest formula is a very useful tool in calculating the future value of an investment, rate of investment, etc using the other information available. It is used in case the interest is earned by the investor on principal as well as previously earned interest part of the investment. In case when the investments are done where the return is earned using compound interest then this type of investment grow quickly as the interest is earned on the previously earned interest as well however one can determine how quickly investment grows only on the basis of the rate of return and number of the compounding periods.

Recommended Articles

This has been a guide to Compound Interest Examples. Here we discuss how to calculate compound interest (Annually, Monthly, Quarterly) using its formula along with practical examples. You may learn more about financial modeling from the following articles –

The Power of Compound Interest and Why It Pays to Start Saving Now

How to Learn About Compound Interest and Investing Using the One‐Penny TrickHave you ever wished that you could have more money, without all the effort? Or are you concerned you won’t have enough saved for retirement or your child’s education?

Luckily, there’s actually a simple way to accomplish those things if you’re willing to learn how to put your money to work for you. It’s called compound interest, and it can help you exponentially grow your wealth.

What Is Compound Interest?

When people think of interest, they often think of debt. But interest can work in your favor when you’re earning it on money you’ve saved and invested.

Compound interest can be defined as interest calculated on the initial principal and also on the accumulated interest of previous periods. Think of it as the cycle of earning “interest on interest” which can cause wealth to rapidly snowball. Compound Interest will make a deposit or loan grow at a faster rate than simple interest, which is interest calculated only on the principal amount.

Not only are you getting interest on your initial investment, but you are getting interest on top of interest! It’s because of this that your wealth can grow exponentially through compound interest, and why the idea of compounding returns is like putting your money to work for you.

Why It’s Important to Save Now

The magic ingredient that makes compound interest work best is time.

The simple fact is that WHEN you start saving outweighs how much you save.

An investment left untouched for a period of decades can add up to a large sum, even if you never invest another dime.

Let’s see how compound interest works with an example. Below, Alice, Barney and Christopher experience the exact same 7% annual investment return* on their retirement funds. The only difference is when and how often they save:

  • Alice invests $5,000 per year beginning at age 18. At age 28, she stops. She has invested for 10 years and $50,000 total.
  • Barney invests the same $5,000 but begins where Alice left off. He begins investing at age 28 and continues the annual $5,000 investment until he retires at age 58. Barney has invested for 30 years and $150,000 total.
  • Christopher is our most diligent saver. He invests $5,000 per year beginning at age 18 and continues investing until retirement at age 58. He has invested for 40 years and a total of $200,000.

(Click for larger image)

Barney has invested 3 times as much as Alice, yet Alice’s account has a higher value. She saved for just 10 years while Barney saved for 30 years. This is compound interest: the investment return that Alice earned in her 10 early years of saving is snowballing. The effect is so drastic that Barney can’t catch up, even if he saves for an additional 20 years.

The best scenario here is Christopher, who begins saving early and never stops. Note how the amount he has saved is massively higher than either Alice or Barney. Is it so astounding that Christopher’s savings have grown so large? Not necessarily – what is most remarkable is how simple his path to riches was. Slow and steady annual investments, and most importantly beginning at an early age.

Compound interest favors those that start early, which is why it pays to start now. It’s never too late to start — or too early.

If you are early in your career, it can feel like there are a lot of things competing for your money between student loans, saving for a house, retirement and more. However, saving now can give you a huge edge on your finances so you can retire stress-free. Also, if you are saving for your child’s education, the power of compound interest surely applies. Start saving when they are in diapers and not as they are starting their college search.

Get Started

If you want to easily accumulate wealth and take advantage of the magic of compound interest, it’s important to start early and be consistent. As you can see in the example above, it’s possible for your money to grow to a large sum with a small initial investment. If you consistently save and invest, you’ll have a nice nest egg by the time you retire.

To get started, you can:

  • Max out your Roth IRA ($6,000 limit in 2019 and $6,500 for age 50 and older)
  • Contribute to your employer-sponsored 401(k), especially if there is a match (that’s free money!)
  • Contribute to an account like a SEP IRA if you’re self-employed; while you may not get a match from an employer, these contributions are tax-deferred
  • If education is your goal, max out a Coverdell IRA ($2,000 limit) or contribute to a 529 plan (limits vary by state but are much higher).

The key is to start now and contribute what you can! It may seem like it’s not worth it, but even small contributions of $25-$100 per month add up over time.

Time is your best friend and the one thing that makes compound interest so effective. Saving now and starting early will pay dividends in your future and help you accumulate extra money. That’s the power of compound interest and why it pays to start saving now.

*A 7% annual return is hypothetical. Past performance is no guarantee of future results. (Even if the hypothetical annual return was reduced, the outcome would still be the same. Alice would still have more savings than Barney, and Christopher would still have the most savings available.)

Windgate does not provide tax advice. Consult your professional tax advisor for questions concerning your personal tax or financial situation.

Data here is obtained from what are considered reliable sources as of 3/31/2019; however, its accuracy, completeness, or reliability cannot be guaranteed.

Let’s Talk

Ready to discuss your financial goals and determine if Windgate might be your solution ?

The rule of 72 is a mathematical shortcut used to predict when a population, investment or other growing category will double in size for a given rate of growth. It is also used as a heuristic device to demonstrate the nature of compound interest. It has been recommended by many statisticians that the number 69 be used, rather than 72, to estimate the results of continuous compounding rates of growth. Calculate how quickly continuous compounding will double the value of your investment by dividing 69 by its rate of growth.

The rule of 72 was actually based on the rule of 69, not the other way around. For non-continuous compounding, the number 72 is more popular because it has more factors and is easier to calculate returns quickly.

Continuous Compounding

In finance, continuous compounding refers to a growth rate with compounding periods that are infinitesimally small; the interest generated is calculated and compounded more than once per second, for example.

Because an investment with continuous compounding grows faster than an investment with simple or discrete compounding, standard time value of money calculations are ill-equipped to handle them.

Rule of 72 and Compounding

The rule of 72 comes from a standard compound interest formula:

This formula makes it possible to find a future value that is exactly twice the present value. Do this by substituting FV = 2 and PV = 1:

Now, take the logarithm of both sides of the equation, and use the power rule to simplify the equation further:

Since 0.693 is the natural logarithm of 2. This simplification takes advantage of the fact that, for small values of r, the following approximation holds true:

The equation can be further rewritten to isolate the number of time periods: 0.693 / interest rate = n. To make the interest rate an integer, multiply both sides by 100. The last formula is then 69.3 / interest rate (percentage) = number of periods.

It isn’t very easy to calculate some numbers divided by 69.3, so statisticians and investors settled on the nearest integer with many factors: 72. This created the rule of 72 for quick future value and compounding estimations.

Continuous Compounding and the Rule of 69(.3)

The assumption that the natural log of (1 + interest rate) equals the interest rate is only true as the interest rate approaches zero in infinitesimally small steps. In other words, it is only under continuous compounding that an investment will double in value under the rule of 69.

If you really want to calculate how quickly an investment will double for a given interest rate, use the rule of 69. More specifically, use the rule of 69.3.

Suppose a fixed-rate investment guarantees 4% continuously compounding growth. By applying the rule of 69.3 formula and dividing 69.3 by 4, you can find that the initial investment should double in value in 17.325 years.

Definition & Examples of Interest

  • Share
  • Pin
  • Email

How to Learn About Compound Interest and Investing Using the One‐Penny Trick

Tetra Images / Getty Images

Interest is the cost of using somebody else’s money. When you borrow money, you pay interest. When you lend money, you earn interest.

Here, you’ll learn more about interest, including what it is and how to calculate how much you either earn or owe depending on whether you lend or borrow money.

What Is Interest?

Interest is calculated as a percentage of a loan (or deposit) balance, paid to the lender periodically for the privilege of using their money. The amount is usually quoted as an annual rate, but interest can be calculated for periods that are longer or shorter than one year.

Interest is additional money that must be repaid in addition to the original loan balance or deposit. To put it another way, consider the question: What does it take to borrow money? The answer: More money.

How Does Interest Work?

There are several different ways to calculate interest, and some methods are more beneficial for lenders. The decision to pay interest depends on what you get in return, and the decision to earn interest depends on the alternative options available for investing your money.

When borrowing: To borrow money, you’ll need to repay what you borrow. In addition, to compensate the lender for the risk of lending to you (and their inability to use the money anywhere else while you use it), you need to repay more than you borrowed.

How to Learn About Compound Interest and Investing Using the One‐Penny Trick

When lending: If you have extra money available, you can lend it out yourself or deposit the funds in a savings account, effectively letting the bank lend it out or invest the funds. In exchange, you’ll expect to earn interest. If you are not going to earn anything, you might be tempted to spend the money instead, because there’s little benefit to waiting.

How much do you pay or earn in interest? It depends on:

  1. The interest rate
  2. The amount of the loan
  3. How long it takes to repay

A higher rate or a longer-term loan results in the borrower paying more.

Example: An interest rate of 5% per year and a balance of $100 results in interest charges of $5 per year assuming you use simple interest. To see the calculation, use the Google Sheets spreadsheet with this example. Change the three factors listed above to see how the interest cost changes.

Most banks and credit card issuers do not use simple interest. Instead, interest compounds, resulting in interest amounts that grow more quickly.

How Do I Earn Interest?

You earn interest when you lend money or deposit funds into an interest-bearing bank account such as a savings account or a certificate of deposit (CD). Banks do the lending for you: They use your money to offer loans to other customers and make other investments, and they pass a portion of that revenue to you in the form of interest.

Periodically, (every month or quarter, for example) the bank pays interest on your savings. You’ll see a transaction for the interest payment, and you’ll notice that your account balance increases. You can either spend that money or keep it in the account so it continues to earn interest. Your savings can really build momentum when you leave the interest in your account; you’ll earn interest on your original deposit as well as the interest added to your account.

Earning interest on top of the interest you earned previously is known as compound interest.

Example: You deposit $1,000 in a savings account that pays a 5% interest rate. With simple interest, you’d earn $50 over one year. To calculate:

  1. Multiply $1,000 in savings by 5% interest.
  2. $1,000 x .05 = $50 in earnings (see how to convert percentages and decimals).
  3. Account balance after one year = $1,050.

However, most banks calculate your interest earnings every day, not just after one year. This works out in your favor because you take advantage of compounding. Assuming your bank compounds interest daily:

  • Your account balance would be $1,051.16 after one year.
  • Your annual percentage yield (APY) would be 5.12%.
  • You would earn $51.16 in interest over the year.

The difference might seem small, but we’re only talking about your first $1,000. With every $1,000, you’ll earn a bit more. As time passes, and as you deposit more, the process will continue to snowball into bigger and bigger earnings. If you leave the account alone, you’ll earn $53.78 in the following year, compared to $51.16 the first year.

See a Google Sheets spreadsheet with this example. Make a copy of the spreadsheet and make changes to learn more about compound interest.

When Do I Have to Pay Interest?

When you borrow money, you generally have to pay interest. But that might not be obvious, as there’s not always a line-item transaction or separate bill for interest costs.

Installment debt: With loans like standard home, auto, and student loans, the interest costs are baked into your monthly payment. Each month, a portion of your payment goes toward reducing your debt, but another portion is your interest cost. With those loans, you pay down your debt over a specific time period (a 15-year mortgage or five-year auto loan, for example).

Revolving debt: Other loans are revolving loans, meaning you can borrow more month after month and make periodic payments on the debt.   For example, credit cards allow you to spend repeatedly as long as you stay below your credit limit. Interest calculations vary, but it’s not too hard to figure out how interest is charged and how your payments work.

Additional costs: Loans are often quoted with an annual percentage rate (APR). This number tells you how much you pay per year and may include additional costs above and beyond the interest charges. Your pure interest cost is the interest rate (not the APR). With some loans, you pay closing costs or finance costs, which are technically not interest costs that come from the amount of your loan and your interest rate. It would be useful to find out the difference between an interest rate and an APR. For comparison purposes, an APR is usually a better tool.

Ryan Vanzo | September 20, 2020 | More on: ENB ENB

You can become a millionaire with just $6,000. To be sure, you also need to have patience and good habits, but with regular saving and the right stocks, your path to $1 million is clear.

The biggest trick is to harness the power of compound interest. Albert Einstein reportedly called this the most powerful force in the universe. At the least, it’s the most powerful force in finance.

The magic of compound interest is that your money will grow faster the longer it’s invested. Gains accrue slowly at first, but over the years, a snowball effect emerges. Down the line, your $6,000 contribution could be generating $50,000 annual gains. That’s quite a feat.

The path to becoming a millionaire on $6,000 isn’t necessarily easy, but it’s surprisingly simple.

Compound your interest

Almost every self-made millionaire has figured out how to make compound interest work for them. Over time, the results can be amazing.

Consider an investment of just $6,000. Using stocks like Enbridge (TSX:ENB)(NYSE:ENB), which has posted double-digit annual gains for decades at a time, you can slowly but surely build a fortune.

Investing $6,000 at a 10% annual rate of return will produce little at the start. After one year you’ll have a profit of $600. But after two years, your profits will total $1,260. You can already start to see your money grow faster over time.

The real magic starts to happen over decades. After 10 years, you’ll net a profit of $9,560. After 20 years, interest will total $34,360. If you wait 40 years, you’ll accumulate a profit of $265,000, all from a measly initial sum of $6,000.

But wait a second … $265,000 doesn’t make you a millionaire, and not everyone can afford to wait 40 years. Thankfully, you can accelerate the timeline by becoming consistent.

Be consistent

Everyone says that they’ll commit to saving more in the future, but few do. It’s a human weakness. That’s too bad considering consistent contributions are a major factor in becoming a millionaire.

Let’s begin with the previous example of contributing $6,000 at the start while earning 10% annual returns. Except this time, you contribute another $6,000 at the end of each year.

By contributing $6,000 every year, you can surpass the quarter-million-dollar mark after just 16 years. In the previous example, where you didn’t follow up with additional contributions, it took 40 years to reach this level.

But what about becoming a millionaire? By investing $6,000 each year, earning 10% per year, you reach the $1 million point after 29 years. That’s not bad, but if you want to speed up the timeline even more, you must choose the right stocks.

Buy millionaire stocks

Generating 10% annual returns is a great start. You can become a millionaire even faster by picking higher-growth stocks.

Hexo (TSX:HEXO)(NYSE:HEXO) is a great example. This $400 million pot stock is capable of doubling, or even tripling in value in the coming years. There’s more risk here, but it could chop a decade or more off your investing horizon.

If you find stocks capable of delivering 20% annual returns, you can become a millionaire in less than two decades. That’s possible by investing just $6,000 per year.

Our top stock pick below can generate 20% annual returns.

5G is one of the greatest arrivals in technology since the birth of the internet. We could see plenty of new wealth-building opportunities in 2020 that would potentially dwarf any that came before them.

5G has the potential to radically change our lives and society as we know it, but if you’re an investor, the implications are even greater — and potentially much more lucrative.

To learn more about it and its revolutionary potential to change the industry — and potentially your bank account — click on the link below to get the full scoop.

The Motley Fool owns shares of and recommends Enbridge. The Motley Fool recommends HEXO. and HEXO. Fool contributor Ryan Vanzo has no position in any stocks mentioned.

23 October 2014

Helping kids to understand the benefit of saving early can reap big rewards.

When trying to teach our young children about the value of compound interest – or the time value of money – one possible place to start is with a small number of marshmallows. Truly.

In the late 1960’s Stanford University psychologist, Walter Mischel ran a series of delayed gratification tests on a total of 653 three to five year-olds. One well-known example was the marshmallow test, whereby each preschool child was left alone in a room with one marshmallow and a promise that if they could refrain from eating the sweet until the researcher returned, they would receive another one. The focus of the test was on the ability of the children to exercise restraint, but it could also work as a good lesson in how compound interest works.

‘Compound interest’ simply means earning interest on your savings and also, eventually, on the interest that those savings earn. The earlier you begin to save, the more compound interest you will earn. An adult example would be, say, $1,000 to save. Investing that $1,000 at an interest rate of 4% p.a. means that at the end of year one, you would have $1,040. During year two, you would be earning interest on a balance of $1,040 – or in other words, earning interest on both your initial savings plus the interest that those saving have already earned.

That example might be beyond our young children, but there are plenty of fun compound interest lessons you might try. An easy step-by-step example is:

  • Give your child a small sweet (or marshmallow). Ask them how long they think they could save it for, before eating it. Offer to give them an additional sweet for each day that they can keep their sweets uneaten. This helps children understand the concept of reward for saving.
  • Then perhaps expand the lesson with coins. Give an initial small amount of money to your child (perhaps fifty cents) and offer to add to the amount each day for as many days as your child can continue to save. Gradually increase the daily amount that you provide (for example, ten cents, then fifteen, then twenty) to mimic compound earnings. Our coin discovery activity sheet could help your child track the progress of their savings.
  • Explain that money in the bank earns interest. Once your child has practiced “saving” their sweets and has grasped the concept of earning more by saving more, you can explain that money invested in a savings account works in a similar way; that the earlier children save, the more compound interest they can earn.

How do you teach your children about the time value of money? Share your tips below, and for more financial literacy articles, visit the Beanstalk.

How to Learn About Compound Interest and Investing Using the One‐Penny Trick

The higher the frequency of compounding, the higher is the maturity value of an investment.

Synopsis

  • Abc Small
  • Abc Normal
  • Abc Large

Simple interest and compound interest are two ways of calculating interest rates. Based on the method of calculation, interest rates are classified as nominal interest rate, effective interest rate and annual percentage yield (APY). The nominal interest rate does not take into account compounding of interest at defined intervals.

The effective interest rate is arrived at after compounding. Compounding can either be monthly, quarterly, biannual, or annual. Although it is not typically offered by investment products, the frequency of compounding can also be weekly or daily. The higher the frequency of compounding, the higher is the maturity value of an investment.

To illustrate, annual interest of 8% on a fixed deposit will translate into an effective interest rate of 8.24%, if the interest is compounded quarterly. If it is compounded biannually, the effective rate will be 8.16%. Here the stated 8% interest is the nominal interest rate. To calculate the maturity value of an investment, you can use the following formula:

Maturity value=(principal) x (1+r)^n
n = investment tenure
r = interest rate

If one uses the nominal rate of 8% in the above formula, the maturity value of Rs 1 lakh invested in a five-year FD, compounded quarterly, works out to be Rs 1,46,933. But this is not the amount you will receive. To find out the right maturity amount, you need to use the effective interest rate.

The correct maturity value, using effective interest rate of 8.24%, works out to be Rs 1,48,595. As the nominal rate does not account for quarterly compounding, it underestimates the maturity amount by Rs 1,662.

If you only have the nominal rate to work with, you can still capture the effects of compounding. Just divide the ‘r’ and multiply the ‘n’ in the above formula by the frequency of compounding.

There is an easier way too. You can use MS Excel’s EFFECT function to automatically converts the nominal rate into the effective rate. The function requires only two inputs, the nominal interest rate, and the compounding frequency (Npery). For example, if the nominal rate is 8%, and the compunding requency is monthly, the effective rate works out to be 0.083 or 8.3%. For monthly compounding, the Npery value will in the EFFECT function will be 12.

Use Excel to calculate effective rate
Just key in nominal rate and compounding frequency in the EFFECT function.

How to Learn About Compound Interest and Investing Using the One‐Penny Trick
It will be 1, 2, 4, 52 and 365 for yearly, biannual, quarterly, weekly and daily compounding respectively. Once you get the effective rate, you can use it in the formula cited earlier to calculate the maturity value of your investment. MS Excel also has NOMINAL function that calculates the nominal rate, based on the effective rate and the compounding frequency.

Don’t get lured by higher annual % yield
APY works out to be higher than the effective rate, despite maturity sum being the same.
How to Learn About Compound Interest and Investing Using the One‐Penny Trick

The effective rate also influences an investment product’s annual percentage yield (APY). It is calculated by dividing the annual interest by the principal amount. APY proves useful when comparing deposits with varying compounding frequencies. But be careful with APY.

Although the maturity value remains unchanged, APY works out to be higher than the effective rate. So, some financial institutions highlight APY to make their investment offerings look more attractive.

To illustrate, using the effective rate of 8.24%, the total interest on an investment of Rs 1 lakh for five years, works out to be Rs 48,595. This is the same as an annual interest of Rs 9,719 over five years. Dividing Rs 9,719 by the principal gives an APY of 9.72%—1.48% higher than the effective interest rate. But this higher APY is of no material significance as the maturity amount at an effective rate of 8.24% and at an APY of 9.72%remains the same— Rs 1.49 lakh.

Tutorial and Worksheet for Teaching Yourself

  • Share
  • Flipboard
  • Email

How to Learn About Compound Interest and Investing Using the One‐Penny Trick

There are two types of interest, simple and compound. Compound interest is interest calculated on the initial principal and also on the accumulated interest of previous periods of a deposit or loan. Learn more about compound interest, the math formula for calculating it on your own, and how a worksheet can help you practice the concept.

More About What Compound Interest Is

Compound interest is the interest you earn each year that is added to your principal, so that the balance doesn’t merely grow, it grows at an increasing rate. It is one of the most useful concepts in finance. It is the basis of everything from developing a personal savings plan to banking on the long-term growth of the stock market. Compound interest accounts for the effects of inflation, and the importance of paying down your debt.

Compound interest can be thought of as “interest on interest,” and will make a sum grow at a faster rate than simple interest, which is calculated only on the principal amount.

For example, if you got 15 percent interest on your $1000 investment the first year and you reinvested the money back into the original investment, then in the second year, you would get 15 percent interest on $1000 and the $150 I reinvested. Over time, compound interest will make much more money than simple interest. Or, it will cost you much more on a loan.

Computing Compound Interest

Today, online calculators can do the computational work for you. But, if you do not have access to a computer, the formula is pretty straightforward.

Use the following formula used to calculate compound interest:

Applying the Formula

For example, let’s say that you have $1000 to invest for three years at a 5 percent compound interest rate. Your $1000 would grow to be $1157.62 after three years.

Here’s how you would get that answer using the formula and applying it to the known variables:

  • M = 1000 (1 + 0.05) 3 = $1157.62

Compound Interest Worksheet

Are you ready to try a few on your own? The following worksheet contains 10 questions on compound interest with solutions. Once you have a clear understanding of compound interest, go ahead and let the calculator do the work for you.

History

Compound interest was once regarded as excessive and immoral when applied to monetary loans. It was severely condemned by Roman law and the common laws of many other countries.

The earliest example of a compound interest table dates back to a merchant in Florence, Italy, Francesco Balducci Pegolotti, who had a table in his book “Practica della Mercatura” in 1340. The table gives the interest on 100 lire, for rates from 1 to 8 percent for up to 20 years.

Luca Pacioli, also known as the “Father of Accounting and Bookkeeping,” was a Franciscan friar and collaborator with Leonardo DaVinci. His book “Summa de Arithmetica” in 1494 featured the rule for doubling an investment over time with compound interest.

Last Updated: June 17, 2020 References

This article was co-authored by Benjamin Packard. Benjamin Packard is a Financial Advisor and Founder of Lula Financial based in Oakland, California. Benjamin does financial planning for people who hate financial planning. He helps his clients plan for retirement, pay down their debt and buy a house. He earned a BA in Legal Studies from the University of California, Santa Cruz in 2005 and a Master of Business Administration (MBA) from the California State University Northridge College of Business in 2010.

There are 10 references cited in this article, which can be found at the bottom of the page.

This article has been viewed 325,125 times.

Compound interest is distinct from simple interest in that interest is earned both on the original investment (the principal) and the interest accumulated so far, rather than simply on the principal. Because of this, accounts with compound interest grow faster than those with simple interest. For example, if your interest compounds annually, that means that you’ll gain more interest in the second year after your investment than you did in the first year. Additionally, the value will grow even faster if the interest is compounded multiple times per year. Compound interest is offered on a variety of investment products and also charged on certain types of loans, like credit card debt. [1] X Research source Calculating how much an amount will grow under compound interest is simple with the right equations.

Learn the basics of investing, how to start managing your portfolio, reduce risk, and make smart decisions

Get ahead of the market by understanding the true value of a stock and capitalizing on its price. Learn fundamental.

Leverage targeted analysis to sift through the thousands of exchange-traded stocks to find the right choices for your growing portfolio.

About the Instructors

Luke served as Head of ETF Sales at Cantor Fitzgerald. While in this seat, he began to notice the importance that institutional trading activity had on the movements and direction of stocks. He spent years observing these activities and in his free time, with a partner, began designing quantitative models to look for unusual trading activity. He later moved to Jefferies, LLC as an SVP of Derivatives. There he published stock research based around the unusual activity signals he was developing. He later left Wall Street to work on this research full time at MAPsignals.com.

John Jagerson is a CFA and CMT charter holder and a founder of Learning Markets, which provides analysis and education for individual and professional investors. He is an author or co-author of five books on investing, currencies, bonds, and stocks. John has appeared in outlets like Forbes.com, BBC Radio, Nasdaq.com, and CBS for his financial strategy expertise. After graduating with a B.S. in Business from Utah Valley University, John completed the PLD program at Harvard Business School. Once the markets close each day, he can be found back on his mountain bike or in his running shoes on the trails of the Wasatch Mountains near his home.

James Early has more than 20 years of experience in institutional finance. After leaving hedge fund TSL Capital, James served as director of research and analysis at Motley Fool, one of the world’s leading Internet investment companies; his 10-year equity advisory track record in the US and London outperformed the S&P 500 and FTSE 100. James is a member of the Wall Street Fintech Club and a DC executive committee member of the Sino-American Pharmaceutical Association, as well as Mensa. James often appears as a special guest on CNN, BBC, CNBC, CCTV, The Wall Street Journal and other international media.

Understanding Compound Interest

  • Share
  • Flipboard
  • Email

How to Learn About Compound Interest and Investing Using the One‐Penny Trick

Don Bishop / Getty Images

Compound interest is important for anyone making investments or repaying loans to understand how to profit the most from interest. Depending on whether compound interest is being earned or paid on a sum, it could either make a person much more money or cost them much more on a loan than simple interest.

What Is Compound Interest?

Compound interest is interest on a principal sum and any of its accrued interest often called interest-on-interest. It is most commonly calculated when reinvesting earnings gained from interest on a sum back into the original deposit, thus greatly increasing the amount gained by the investor.

Simply put, when interest is compounded, it is added back into the original sum.

Calculating Compound Interest

The formula used to calculate compound interest is M = P( 1 + i )n. M is the final amount including the principal, P is the principal amount (the original sum borrowed or invested), i is the rate of interest per year, and n is the number of years invested.

For example, if a person got 15% interest on a $1,000 investment during the first year—totaling $150—and reinvested the money back into the original investment, then in the second year, the person would get 15% interest on $1,000 and the $150 that was reinvested.

Practice Making Compound Interest Calculations

Understanding how compound interest is calculated can help when determining payments for loans or the future values of investments. These worksheets provide many realistic compound interest scenarios that allow you to practice applying interest formulas. These practice problems, along with strong background knowledge in decimals, percentages, simple interest, and interest vocabulary, will prepare you for success when finding compound interest values in the future.

Answer keys can be found on the second page of each PDF.

Compound Interest Worksheet #1

Print this compound interest worksheet to support your understanding of the compound interest formula. The worksheet requires you to plug the correct values into this formula to calculate interest on loans and investments that are mostly compounded annually or quarterly.

You should review the compound interest formulas to help you determine what values are required for calculating each answer. For additional support, the United States Securities and Exchanges Commission website features a useful calculator for finding compound interest.

The future value formula helps you calculate the future value of an investment (FV) for a series of regular deposits at a set interest rate (r) for a number of years (t).

Using the formula requires that the regular payments are of the same amount each time, with the resulting value incorporating interest compounded over the term.

How to Learn About Compound Interest and Investing Using the One‐Penny Trick

In this article we’ll delve into the formulae available and then go through a couple of examples. At the bottom of this article, you’ll find an interactive formula, which will allow you to enter figures of your choosing and see how the calculation is made. Should you wish to read it, we also have an article discussing the compound interest formula.

Future value of a series formula

A = PMT × (((1 + r/n)^(nt) – 1) ÷ (r/n))

The formula above assumes that deposits are made at the end of each period (month, year, etc). Below is a variation for deposits made at the beginning of each period:

Alternative formula:

A = PMT × (((1 + r/n)^(nt) – 1) ÷ (r/n)) × (1+r/n)

A = the future value of the investment, including interest
PMT = the payment amount per period
r = the annual interest rate (decimal)
n = the number of compounds per period
t = the number of periods the money is invested for
^ means ‘to the power of’

Future value formula example 1

An investment is made with deposits of $100 per month (made at the end of each month) at an interest rate of 5%, compounded monthly (so, 12 compounds per period). The value of the investment after 10 years can be calculated as follows.

PMT = 100. r = 5/100 = 0.05 (decimal). n = 12. t = 10.

If we plug those figures into formula 1, we get:

Total = [ PMT × (((1 + r/n)^nt – 1) ÷ (r/n)) ]
Total = [ 100 × (((1 + 0.0041 6 )^(120) – 1) ÷ (0.0041 6 )) ]
Total = [ 100 × (0.647009497690848 ÷ 0.0041 6 ) ]
Total = [ 15528.23 ]

So, the investment figure after 10 years will stand at $15,528.23.

Future value formula example 2

An individual decides to invest $10,000 per year (deposited at the end of each year) at an interest rate of 6%, compounded annually. The value of the investment after 5 years can be calculated as follows.

PMT = 10000. r = 6/100 = 0.06 (decimal). n = 1. t = 5.

Total = [ PMT × (((1 + r/n)^(nt) – 1) ÷ (r/n)) ]
Total = [ 10000 × (((1 + 0.06)^5 – 1) ÷ 0.06) ]
Total = [ 10000 × (0.3382255776 ÷ 0.06) ]
Total = [ 10000 × 5.63709296 ]
Total = [ 56370.9296 ]

Our investment balance after 5 years is therefore $56,370.93. This would be comprised of $50,000 in investment and $6,370.93 in interest.

Interactive future value formula

Use the calculator below to show the formula and resulting calculation for your chosen figures. Note that this calculator requires JavaScript to be enabled in your browser. Also, note that ^ means ‘to the power of’

Should you wish to have a visual breakdown of deposits and interest over time, give our compound interest calculator a try.

Rate this article

Please rate this article below. If you have any feedback on it, please contact me.

Grow Your Business, Not Your Inbox

How to Learn About Compound Interest and Investing Using the One‐Penny Trick

Personal finance is important. Starting a smart personal finance plan as soon as possible can mean the difference between retiring early, sending your kids to their dream schools and more. But, before you can save big bucks, you need to know the basics of personal finance. In this video, Entrepreneur Network partner Phil Town helps you by explaining how compound interest — one of the most important aspects of personal finance — works.

When interest is compounded, rather than paid linearly, the overall size of the investment grows exponentially faster. The effects are harder to see in the early years, but eventually, they become quite pronounced.

Click play to learn more.

Entrepreneur Network is a premium video network providing entertainment, education and inspiration from successful entrepreneurs and thought leaders. We provide expertise and opportunities to accelerate brand growth and effectively monetize video and audio content distributed across all digital platforms for the business genre.

EN is partnered with hundreds of top YouTube channels in the business vertical. Watch video from our network partners on demand on Roku, Apple TV and the Entrepreneur App available on iOS and Android devices.

Click here to become a part of this growing video network.

Use our home loan repayment calculator to find out how much your ongoing mortage repayments could be, and the amount of interest you’ll need to pay over the life of your home loan. Simply:

  1. Enter your loan details (including the loan amount, loan period, type of loan, interest rate and repayment information)
  2. Review your results.

Want to be debt free?

Important information

Note: The results from this calculator should be used as an indication only. Results do not represent either quotes or pre-qualifications for a loan. It is advised that you consult your financial adviser before taking out a loan.

  • This calculator is provided by Widget Works.
  • The results shown in this calculator are estimates only and are not guaranteed by AMP Bank. They are based on the accuracy of the data entered into the calculator.
  • Other than as required by consumer protection law, under no circumstances will AMP Bank and its related bodies corporate be liable for any loss and/or damage caused by a user’s reliance on information obtained by using this calculator.
  • AMP Bank and its related bodies corporate specifically disclaim any liability (whether based in contract, tort, strict liability or otherwise) for any direct, indirect, incidental, consequential or special loss and/or damages arising out of or in any way connected with the access to or use of this calculator.
  • Any change to the factors used in the calculation would vary the results.
  • The calculator and the results provided are generic and do not take into account your personal circumstances. The calculator is a guide only and is not intended to be relied upon for the purposes of making a decision in relation to a credit or financial product. The user should obtain professional financial advice before making any financial decision.
  • Any advice given is general advice only and has been prepared without taking account of your objectives, financial situation or needs. Given this, before acting on the advice, you should consider the appropriateness of the advice having regard to your objectives, financial situation and needs before acting on it. Consider the applicable Terms and Conditions before deciding whether to acquire or continue to hold an AMP Bank product.
  • The calculator is not an offer for a loan. To apply for an AMP Bank home loan, you must complete an application form and submit it together with all required documentation for assessment. Formal loan approval is subject to AMP Bank lending criteria. All information entered into the calculator will require verification as part of our application process.
  • When taking out an AMP Bank loan, certain fees and charges are payable by the borrower. These include but are not limited to Government stamp duty and registration costs, AMP Bank’s Establishment Fee, Lender’s Mortgage Insurance and other fees and charges.
  • Fees and charges are payable. Terms and Conditions apply to AMP Bank products and are available upon request.
  • The credit provider and product issuer is AMP Bank Limited ABN 15 081 596 009, Australian credit licence 234517, AFSL 234517.

* The comparison rate is calculated for a secured loan on a loan amount of $150,000 over a 25-year term. WARNING: This comparison rate is true only for the examples given and may not include all fees and charges. Different terms, fees or other loan amounts might result in a different comparison rate.

Learn the basics of investing, how you can start, and guiding principles that can help you along the way.

How to Learn About Compound Interest and Investing Using the One‐Penny Trick How to Learn About Compound Interest and Investing Using the One‐Penny Trick How to Learn About Compound Interest and Investing Using the One‐Penny Trick

Investing basics

New to investing? Find answers to frequently asked questions.

Start your investing journey

How to Learn About Compound Interest and Investing Using the One‐Penny Trick

Create and monitor a portfolio, and get help any time you need it.

How to Learn About Compound Interest and Investing Using the One‐Penny Trick

Simplify the process of investing. Robo-advisors are online services that provide automated portfolios based on your goals and risk tolerance, using the latest technology and expertise from investment professionals.

How to Learn About Compound Interest and Investing Using the One‐Penny Trick

It doesn’t matter if you have $1K or $100K.

It’s a common myth that you need a fortune to start investing.

7 guiding principles

As an investor, you need guiding principles to help you navigate changing markets and different financial decisions in your life journey. Schwab’s Investing Principles are seven clear steps we believe are foundational to successful investing.

How to Learn About Compound Interest and Investing Using the One‐Penny Trick How to Learn About Compound Interest and Investing Using the One‐Penny Trick How to Learn About Compound Interest and Investing Using the One‐Penny Trick

Take the next step.

We can help.

Investing involves risk, including loss of principal.

The information on this website is for educational purposes only. It is not intended to be a substitute for specific individualized tax, legal, or investment planning advice. Where specific advice is necessary or appropriate, please consult with a qualified tax advisor, CPA, financial planner or investment manager.

The Charles Schwab Corporation provides a full range of brokerage, banking and financial advisory services through its operating subsidiaries. Its broker-dealer subsidiary, Charles Schwab & Co., Inc. (Member SIPC), offers investment services and products, including Schwab brokerage accounts. Its banking subsidiary, Charles Schwab Bank, SSB (member FDIC and an Equal Housing Lender), provides deposit and lending services and products. Access to Electronic Services may be limited or unavailable during periods of peak demand, market volatility, systems upgrade, maintenance, or for other reasons.

This site is designed for U.S. residents. Non-U.S. residents are subject to country-specific restrictions. Learn more about our services for non-U.S. residents.

© 2020 Charles Schwab & Co., Inc. All rights reserved. Member SIPC . Unauthorized access is prohibited. Usage will be monitored.

How to Learn About Compound Interest and Investing Using the One‐Penny Trick

How to Learn About Compound Interest and Investing Using the One‐Penny Trick

Do you know that feeling when you leave money in your jacket pocket, only to find it years later? The excitement and euphoria you experience because now you’re $10 richer than you thought? That’s exactly what compound interest is like. Unlike that crumpled tener in your pocket though, the phenomenon of compound interest can be lived over and over again.

Truth is, too many people plan on “living now and saving later”. The idea of investing is some vague, far off concept that only applies to bankers or old people with a lot of money.

I used to work in the mail room for a company that had a 401k program that matched contributions up to 5%. Most of my coworkers didn’t take advantage of this. Not only could they get out of paying taxes on 5% of their paycheck, but their company was offering them FREE MONEY if they just stashed it somewhere safe. FREE MONEY. But shockingly, there were few takers.

It sounds crazy like that, but it’s a lot more common than you might think. When you’re making less money and budgets are tight, taking 5% of your paychecks and putting it away can seem pretty hard to do. Heck, even if you do have money to spare, who wants to invest in a 401k in their 20s? Retirement is decades away! Spend your money on living now and wait until you’re older to start thinking about saving, right?

Wrong. That’s the opposite of an ideal approach, thanks to one simple yet powerful concept: compound interest.

Compound Interest: Defined

Compound interest is a reference to the way that your money starts growing at an exponential rate over time. In simplest terms, compound interest is the growth you experience once you’ve reinvested the compound interest you received on your initial investment.

Compound Interest: Explained

For example, let’s say you put down $10 of your paycheck and invest it evenly across the S&P 500. The S&P 500, over time, generally returns about 10% a year. So, $10 for stock today and you’ll hypothetically be looking at $11 worth of stock next year. What if you then leave it in there for another year? Another $1 gain and you’re looking at $12, right? Wrong. The 10% gain that next year is on the now $11 worth of stock, so you’re actually picking up $1.10. The following year, it’s 10% on $12.10, meaning you’re making $1.21. Keep at it, year after year, and you start to see that initial $10 grow exponentially.

Obviously, stocks aren’t nearly that consistent. Some years they’ll grow way more and others they’ll actually lose value, but over the long run, the end results remain the same. The lowest the index has ever returned over a 25-year period, ups and downs included, is 9.28%.

Try using a compound interest calculator to see things in action. As an example, if you put in $10 for 30 years, your investment will grow to nearly $175, which is more than 17x the money you put in initially!

The Greater the Investment, The Higher the Compounding

Now imagine our previous example, but with higher sums of money. Now you’re 25 and manage to scrape together $1,000 a year over the next ten years. That’s just $83.33 a month, which is less than your cable bill in most cases. You then spend the back half of your 30s, and all of your 40s and 50s living dangerously and spending every penny you make. With a 10% return and retirement at age 65, you’ll be looking at $323,346.67. Boom.

Let’s compare that previous example with someone who lives it up while they’re young and then gets serious at age 55. Let’s say they contribute $5,000 a year from there on out. By the time they’re 65, they’ve earned just shy of $180,000. This turns out to be about half of the earnings, despite making 5x the contribution than in the previous example!

As another example, what would happen if you invested $10,000 with a 10% return, without making any other contributions the rest of your life? You’re looking at over $450,000 in 40 years! That’s about 40% more than the person making regular contributions starting from 30 years old and nearly 3x what the person starting at 55 years old trying to make up for lost time is looking at.

If you can’t squeeze a regular contribution out of your paycheck, consider putting that windfall away as it comes. Stumble into an inheritance, or get a much bigger check than you’re expecting after filing your tax returns? Even in set-it-and-forget-it mode, you’re much better off taking the plunge now than you would be trying to compensate later in life.

The main takeaway here is the idea that making room to invest later in life is sort of like trying to swim upstream. If anything, you’re much better off setting a smaller sum away now than pumping large sums in later in life when it seems easier.

By investing some money early on, you can help set yourself up for a successful future. Is that as much fun blowing that $10,000 on an expensive trip to Europe or extra rent on your overpriced Brooklyn loft? Absolutely not, at least not in the short-term. The satisfaction comes when you hit your 40s, 50s, and beyond to discover that you can afford to buy the perfect home you’ve always envisioned, send your kids to the college of their dreams, and retire comfortably and sooner than you ever imagined.

Bottom line: the power of compound interest is too valuable to pass up on. No matter what amount you have to spare, investing now is the first step to building a better future for tomorrow.

Interested in learning more about investing? Download the Voleo app and we’ll walk you through the process!

How to Learn About Compound Interest and Investing Using the One‐Penny Trick

This article was written by Mirah Gocher, social media coordinator and investing blogger at Voleo. For the original post, click here.

If you’re interested in expanding your financial literacy further, read the Voleo Investment Community Blog ! Here are some more resources you can use:

This article is for informational purposes only and should not be considered Financial or Legal Advice. None of the opinions expressed by Voleo or participating guests should be construed as investment advice. Securities offered through Voleo USA, Inc. Member of Financial Industry Regulatory Authority (FINRA), Securities Investor Protection Corporation (SIPC). Security products are not FDIC insured, not bank guaranteed, and will fluctuate in value. We do not solicit, recommend, or offer investment advice. Voleo USA, Inc. is a wholly owned subsidiary of Voleo, Inc.

How to Learn About Compound Interest and Investing Using the One‐Penny Trick

Choose the right account for your savings

For short-term goals

As we mentioned above, for an emergency fund and short-term goals (less than five years), it makes sense to hold cash rather than invest it in the markets. Because there is volatility in the markets, you could suffer losses in the short-term and not have cash on hand when you need it. But not all accounts for your short-term cash are created equal. The interest rates of checking or savings accounts can vary widely from a measly 0.01% to a much more attractive 2%. For your short-term cash needs, we recommend using a high-yield savings account with a high interest rate because it allows you to earn a some return without taking on market risk.

For long-term goals

The rest of the savings that you’re holding for long-term expenses (five years or more) should be invested in the market. Which account you choose to invest this cash depends on your goals.

Consider specific tax-advantaged accounts if you’re:

  • Saving for your kid’s college: Experts consider 529 plans the best way to save for college because of their superior tax benefits and relative flexibility. Learn more →
  • Saving for retirement: Consider contributing to a 401(k) if your employer offers matching contributions. Otherwise, an IRA account could offer tax benefits to those who qualify. But in many cases, it may be more advantageous to put retirement savings in a taxable investment account. Read more →

For all other goals, like saving for a downpayment or growing your savings for future expenses, a taxable investment account is likely the best option for you because it’s a flexible account without any withdrawal penalties.

Modified date: April 29, 2019

Student loan debt. Lousy job prospects for recent grads. Wage stagnation. High costs of living.

Do you ever feel like — when it comes to getting ahead financially — the deck is stacked against you?

True, it’s not easy being a 20-something in today’s economy. But you have one thing going for you that has your Baby Boomer parents jealous.

If you’re under the age of 35, you have one of the biggest advantages out there when it comes to planning for eventual financial freedom.

How much you can put away per month is important but, as the numbers below show, that number pales in comparison to how much time you can invest in your plan. In other words, the sooner you start, the greater the advantage you’ll have.

Don’t believe it?

Check out the chart below, which plots the savings strategies of three fictional investors, each of whom saved the same amount of money over a 10-year term.

Through an incredible stroke of investment luck, each earned the same average annual return (seven percent) consistently, until age 65. The only difference between these investors is the year when they start socking away their funds. If you ever plan to retire (and who doesn’t), you should be amazed by the results.

How to Learn About Compound Interest and Investing Using the One‐Penny Trick

The data doesn’t lie

Michael saved $1,000 per month from the time he turned 25 until he turned 35. Then he stopped saving but left his money in his investment account where it continued to accrue at a seven percent rate until he retired at age 65.

Jennifer held off and didn’t start saving until age 35. She put away $1,000 per month from her 35th birthday until she turned 45. Like Michael, she left the balance in her investment account, where it continued to accrue at a rate of seven percent until age 65.

Sam didn’t get around to investing until age 45. Still, he invested $1,000 per month for 10 years, halting his savings at age 55. Then he also left his money to accrue at a seven percent rate until his 65th birthday.

Michael, Jennifer, and Sam each saved the same amount — $120,000 — over a 10 year period.

Sadly for Jennifer, and even more so for Sam, their ending balances were dramatically different.

Saver Ending Balance
Michael $1,444,969
Jennifer $734,549
Sam $373,407

How on earth can I save that much?

I know what some of you are thinking. $1,000 per month sounds like an awful lot for a 25-year-old to save. I hear you. It is a lot. But, it’s not as much as you think.

According to the National Center for Education Statistics, the median annual earnings for a college-educated young adult (aged 25-34) is $46,900. At that income level, a $12,000 annual investment represents 25.5 percent of income. That’s no small percentage of the pie, but that’s before the tax advantages of your employer’s retirement plan are considered.

If your employer offers a 401(k), 403(b), or some other tax-advantaged retirement plan, the money you put away is invested on a pre-tax basis. This means you won’t pay income taxes on your retirement savings until you take the money out at retirement (when your income and therefore your tax burden are likely to be lower).

What does this mean for you now, in the immediate present?

If you’re putting away $12,000 a year in your company’s 401(k) plan, you’re not actually losing that full amount from your take-home pay. Instead, assuming you’re paid every two weeks, your take-home pay will reflect a $346 decrease, assuming you’re a single tax filer in the 25 percent tax bracket.

Thanks to the power of compound interest (the investing magic that allows investment earnings to earn interest of its own), time is the most powerful variable a young investor has on his or her side. Sure, your baby boomer parents might bring home a much higher income, but if you start now, the amount you’ll have to save to fund your retirement is dramatically lower.

Almost $350 per pay period isn’t chump change, for sure, but it is do-able. In fact, do it for 10 years and you might choose to never do it again. You might not have to.

Read More:

  • How Much Should Be In Your 401(k) at Thirty?
  • How Much Should You Contribute to Your 401(k)?
  • Can I Cash Out My Old 401(k)?

Recommended Investing Partners

  • Recommended M1 Finance gives you the benefits of a robo-advisor with the control of a traditional brokerage. M1 charges no commissions or management fees, and their minimum starting balance is just $100. Visit Site

No Minimum Low-fee robo-advisor with no minimum investment. Creates fully-automated portfolios based upon your desired allocation. Visit Site

$500 Minimum Wealthfront requires a $500 minimum investment and charges a very competitive fee of 0.25% per year on portfolios over $10,000. Visit Site