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What Is Compound Interest? Formula & Examples

November 16, 2021 · 6 minute read

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What Is Compound Interest? Formula & Examples

Compound interest is a force to be reckoned with—its power is pretty amazing. It explains why the money you invest today—even a seemingly modest amount—can go so much further than the same sum invested years later.

You’ve probably heard that you should start saving and investing as early as possible, especially for retirement. That sounds like good advice, but we all have other financial priorities. That’s especially true for younger people dealing with mounting student loan debt, higher housing costs, and stagnating salaries. Why is it really so important to put money into the market sooner rather than later?

Because the longer you invest, the more time you have to weather the inevitable ups and downs of the stock market. And the more time your earnings have to compound.

Below, we describe exactly what compound interest is and how it works. Chances are this knowledge may make you want to be the early bird that catches the worm when it comes to investing.

What is Compound Interest?

Compound interest is a method by which the interest an individual can earn is added to their initial investments (the principal). Future interest payments are calculated using that combination (the principal plus interest). Pretty simply, compound interest is the interest earned on their interest. It can allow individuals to build savings, as the initial investment and interest payments grow at an ever increasing rate.

But, before delving too deeply into the ins and outs of compounding interest, it might be helpful, first, to review simple interest.

Simple Interest vs Compound Interest

When an individual deposits money in the bank for one year and the bank pays them interest on that deposit, this is an example of simple interest. Individuals may also encounter simple interest when dealing with short-term loans, such as personal loans. In these instances, interest is calculated by multiplying the principal (the amount deposited or borrowed) by the interest rate and time periods.

Let’s take a look at an example that can clear up how simple interest works. If an individual deposits $100 and the interest rate on their savings or checking account is 5%, they’ll have $105 at the end of the year. They will have earned $5 in interest on top of the initial principal of $100.

It’s not until year two, though, that this individual would start to see the effects of compounding interest. At the beginning of the second year, the individual would start with $105 in the account. This amount will be used in the interest calculation at the end of the year, at which point the individuals will have $110.25 in their account—aka $105 plus $5.25, or 5% of the principal and already earned interest.

So, at the end of year two, they will have earned an additional 5%. The process begins again in year three, at which point the interest payment will be $5.51—or, 5% of the $110.25 saved thus far. With compounding, the size of the interest payment increases each year. And, at the end of three years, the individual has made $15.76, without ever lifting a finger.

It’s worth noting here that interest can compound at different rates depending on the type of account a person holds or how they opt to invest the money. In the banking example above, interest compounds annually. But, in other investment scenarios, interest could compound monthly, daily, or even continuously. The more frequently interest compounds, the more an individual stands to earn.

The Compound Interest Formula

If you want to get technical, there’s a compounding interest formula you can use to calculate returns:

A = P(1+r/n)nt

Let’s break this down. “A” is the final amount of money you’ll end up with. “P” is the principal, or original amount invested. The “r” is the interest rate as a decimal, so 0.1 for 10%. The “n” is the number of times interest compounds each year, and “t” is the number of years you’re looking at.

The “n” in the formula above—how often interest gets compounded—makes a big difference. If interest is compounded monthly instead of yearly, for example, that can really change things.

Compound Interest Example

For example, as a hypothetical scenario, if $5,000 is invested and receives 10% interest that compounded annually, after the first year, the account would earn $500. But starting with the second year, the 10% interest would be calculated based on the new amount of $5,500, not just the original $5,000.

Future Value of $5,000 Investment Compounded Yearly at 10%

Year

Investment

Interest Earned (10%)

New Balance
1 $5000 $500 $5500
2 $5500 $550 $6050
3 $6050 $605 $6650
4 $6650 $665.50 $7310.50
5 $7310.50 $731.55 $8042.05
6 $8042.05 $804.21 $8846.26
7 $8846.26 $884.63 $9730.89
8 $9730.89 $973.09 $10703.98
9 $10703.98 $1070.40 $11774.38
10 $11774.38 $1177.44 $12951.82

The numbers add up quickly. After 10 years, the account would be worth around $12,951.82. (If you want to see how this works for yourself, an online compound interest calculator can generate hypothetical results depending on the initial investment, interest rate, additional contributions, and length of time.)

The Rule of 72

Another simple and helpful formula that might be used to estimate compound interest is known as the Rule of 72. This calculation can allow individuals to look at their rate of return, estimating how long it may take before they double their money (with a fixed rate).

For the Rule of 72, it’s possible to divide 72 by the fixed interest rate. In this sort of calculation, the interest rate percentage would be represented by a numeral—not as a decimal). Say an individual has $1,000 that they want to save at a 3% interest rate. To use the Rule of 72, they might divide 72 by the numeral three to find that it could take 24 years to double the principal at this rate.

The Rule of 72 could be a useful tool when deciding quickly between investment products that offer different possible returns.

Why Making Additional Contributions Matters

While investing early helps you take advantage of compound interest, so does investing regularly. If you make additional contributions each year on top of your initial investment, compounding interest has the chance to go even further.
Getting in on compound interest doesn’t mean you need to have $5,000 to invest today. Even small contributions can make a difference. The earlier you start investing and the more time you have, the more of a chance compound interest has to work its magic.

To illustrate, let’s revisit the equation above with a smaller hypothetical initial investment. Let’s say $500 is contributed to a retirement account today, compounded annually at 10%, and nothing else was done for 10 years. At the end of that time, the account would have:

A = 500 (1+0.1/1)(1*10)
A = 500 * 1.110
A = 500 * 2.5937424601
A = $1,296.87

But if you have 40 years, you get a different answer:

A = 500 (1+0.1/1)(1*40)
A = 500 * 1.140
A = 500 * 45.2592555682
A = $22,629.63

That’s quite a jump! And all it took was time.

If you were also to add just $50 a month to that initial $500 contribution, you’d have around $10,860 in 10 years. And after 40 years? You’d have $288,185.1 Even investing small amounts, especially consistently over time, can pay off, depending on the rate of interest, compound interest.

Making the Most of Compound Interest

Compound interest, on its own, can boost savings. Yet, there are other ways individuals can make more out of this financial strategy.

•  Saving early and often: Time is compound interest’s “special sauce.” Compounding interest grows exponentially over time. So, the longer an individual can leave their money untouched, the more potential it has to grow.

As a result, savers might want to start saving or investing as early as they can. Some tips to think over include:

•  Making additional contributions: Whenever they’re possible, extra contributions add to an individual’s principal (the money that accrues earnings), increasing the total savings on which they’ll gain interest and speeding up their potential financial goals.

Consider an investor who tucks away $1,000 for 20 years at a 6% return (compounding annually). At the end of that period, the investor will have roughly $3,200. If the same investor made an additional monthly contribution of $100, at the end of the period they could have over $47,000.

•  Avoiding making withdrawals: Removing money from an account slows the effects of compounding interest, as it reduces the amount of money on which an individual could earn returns.

•  Checking interest and return rates: The higher the rate of the return, the greater the impact it will have on an individual’s savings. Individuals may want to consider this factor when choosing savings accounts (or other financial products). The average savings account offers relatively low interest rates—around 0.07% in January of 2021 .

Investors seeking a higher return on their investment may opt to turn to high-yield accounts— such as, CDs or the stock market. Stock market investments may offer much higher returns, up to an average of 10% (but there’s always the risk that an individual’s investments will lose money, given market volatility.)

Taking Advantage of Compound Interest with SoFi Invest®

If you want to start making compound interest work for you, you can begin investing online through SoFi Invest. You can get started with as little as $1.

You can invest in a retirement account (traditional, Roth, or SEP IRA) or through an after-tax account. Your funds will go into a portfolio of Exchange-Traded Funds, a lower-cost and more diversified investing strategy.

SoFi’s credentialed financial advisors will rebalance your portfolio at least quarterly to make sure it matches your risk tolerance and investment trajectory.

Learn more about how SoFi Invest can help both novice and sage investors.


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The information provided is not meant to provide investment or financial advice. Investment decisions should be based on an individual’s specific financial needs, goals and risk profile.
1IMPORTANT: The projections and other information included above regarding the likelihood of various investment outcomes are hypothetical in nature, do not reflect actual investment results and are not guarantees of future results.
The information and analysis provided through hyperlinks to third party websites, while believed to be accurate, cannot be guaranteed by SoFi. Links are provided for informational purposes and should not be viewed as an endorsement.
Advisory services offered through SoFi Wealth, LLC a registered investment advisor. SoFi Securities, LLC, member FINRA / SIPC .
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