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# The Power of Compound Interest: Calculations and Examples

## What Is Compound Interest?

Compound interest is the interest on savings calculated on both the initial principal and the accumulated interest from previous periods.

"Interest on interest," or the power of compound interest, is believed to have originated in 17th-century Italy. It will make a sum grow faster than simple interest, which is calculated only on the principal amount.

Compounding multiplies money at an accelerated rate and the greater the number of compounding periods, the greater the compound interest will be.

### Key Takeaways

• Compound interest is interest calculated on the initial principal, which also includes all of the accumulated interest from previous periods.
• Generating "interest on interest" is known as the power of compound interest.
• Interest can be compounded on any given frequency schedule, from continuous to daily to annually.
• Compounding multiplies money at an accelerated rate.
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## How Compound Interest Works

Compound interest is calculated by multiplying the initial principal amount by one plus the annual interest rate raised to the number of compound periods minus one. The total initial amount of the loan is then subtracted from the resulting value.

The formula for calculating the amount of compound interest is as follows:

• Compound interest = total amount of principal and interest in future (or future value) minus principal amount at present (or present value)
= [P (1 + i)n] – P
= P [(1 + i)n – 1]

Where:

P = principal
i = nominal annual interest rate in percentage terms
n = number of compounding periods

Take a three-year loan of \$10,000 at an interest rate of 5% that compounds annually. What would be the amount of interest? In this case, it would be:

\$10,000 [(1 + 0.05)3 – 1] = \$10,000 [1.157625 – 1] = \$1,576.25

## The Power of Compound Interest

Because compound interest includes interest accumulated in previous periods, it grows at an ever-accelerating rate. In the example above, though the total interest payable over the three years of this loan is \$1,576.25, the interest amount is not the same for all three years, as it would be with simple interest. The interest payable at the end of each year is shown in the table below.

Compound interest can significantly boost investment returns over the long term. While a \$100,000 deposit that receives 5% simple annual interest would earn \$50,000 in total interest over 10 years, the annual compound interest of 5% on \$10,000 would amount to \$62,889.46 over the same period. If the compounding period were instead paid monthly over the same 10-year period at 5% compound interest, the total interest would instead grow to \$64,700.95.

## Compound Interest Schedules

Interest can be compounded on any given frequency schedule, from daily to annually. There are standard compounding frequency schedules that are usually applied to financial instruments.

The commonly used compounding schedule for savings accounts at banks is daily. For a certificate of deposit (CD), typical compounding frequency schedules are daily, monthly, or semiannually; for money market accounts, it’s often daily. For home mortgage loans, home equity loans, personal business loans, or credit card accounts, the most commonly applied compounding schedule is monthly.

There can also be variations in the time frame in which the accrued interest is credited to the existing balance. Interest on an account may be compounded daily but only credited monthly. It is only when the interest is credited, or added to the existing balance, that it begins to earn additional interest in the account.

Some banks also offer something called continuously compounding interest, which adds interest to the principal at every possible instant. For practical purposes, it doesn’t accrue that much more than daily compounding interest unless you want to put money in and take it out on the same day.

More frequent compounding of interest is beneficial to the investor or creditor. For a borrower, the opposite is true.

### Compounding Periods

When calculating compound interest, the number of compounding periods makes a significant difference. The basic rule is that the higher the number of compounding periods, the greater the amount of compound interest.

The following table demonstrates the difference that the number of compounding periods can make for a \$10,000 loan with an annual 10% interest rate over a 10-year period.

## Compound Interest: Start Saving Early

Young people often neglect to save for retirement. For people in their 20s, the future seems so far ahead that other expenses feel more urgent. Yet these are the years when compound interest is a game-changer: Saving small amounts can pay off massively down the road—far more than saving higher amounts later on in life. Here's one example of its effect.

Let’s say you start investing in the market at \$100 a month while still in your 20s. Then let’s posit that you average a positive return of 1% a month (12% annually), compounded monthly across 40 years. Now let’s imagine that your twin, who is the same age, doesn’t begin investing until 30 years later. Your tardy sibling invests \$1,000 a month for 10 years, averaging the same positive return.

When you hit your 40-year savings mark—and your twin has saved for 10 years—your twin will have generated about \$230,000 in savings, while you will have a bit more than \$1.17 million. Even though your twin was investing 10 times as much as you (and even more toward the end), the miracle of compound interest makes your portfolio significantly bigger, here by a factor of a little more than five.

The same logic applies to opening an individual retirement account (IRA) and/or taking advantage of an employer-sponsored retirement account, such as a 401(k) or 403(b) plan. Start it in your 20s and be consistent with your payments into it. You’ll be glad you did.

## Pros and Cons of Compounding

Though the miracle of compounding has led to the apocryphal story of Albert Einstein calling it the eighth wonder of the world or man’s greatest invention, compounding can also work against consumers who have loans that carry very high-interest rates, such as credit card debt. A credit card balance of \$20,000 carried at an interest rate of 20% compounded monthly would result in a total compound interest of \$4,388 over one year or about \$365 per month.

On the positive side, compounding can work to your advantage when it comes to your investments and be a potent factor in wealth creation. Exponential growth from compounding interest is also important in mitigating wealth-eroding factors, such as increases in the cost of living, inflation, and reduced purchasing power.

Mutual funds offer one of the easiest ways for investors to reap the benefits of compound interest. Opting to reinvest dividends derived from the mutual fund results in purchasing more shares of the fund. More compound interest accumulates over time and the cycle of purchasing more shares will continue to help the investment in the fund grow in value.

Consider a mutual fund investment opened with an initial \$5,000 and an annual addition of \$2,400. With an average annual return of 12% over 30 years, the future value of the fund is \$798,500. Compound interest is the difference between the cash contributed to the investment and the actual future value of the investment. In this case, by contributing \$77,000, or a cumulative contribution of just \$200 per month, over 30 years, compound interest is \$721,500 of the future balance.

Of course, earnings from compound interest are taxable, unless the money is in a tax-sheltered account. It’s ordinarily taxed at the standard rate associated with your tax bracket and if the investments in the portfolio lose value, your balance can drop.

## Compound Interest Investments

An investor who opts for a dividend reinvestment plan (DRIP) within a brokerage account is essentially using the power of compounding in whatever they invest.

Investors can also experience compounding interest with the purchase of a zero-coupon bond. Traditional bond issues provide investors with periodic interest payments based on the original terms of the bond issue and because these are paid out to the investor in the form of a check, the interest does not compound.

Zero-coupon bonds do not send interest checks to investors. Instead, this type of bond is purchased at a discount to its original value and grows over time. Zero-coupon-bond issuers use the power of compounding to increase the value of the bond so it reaches its full price at maturity.

Compounding can also work for you when making loan repayments. Making half your mortgage payment twice a month, for example, rather than making the full payment once a month, will end up cutting down your amortization period and saving you a substantial amount of interest.

## Tools for Calculating Compound Interest

If it’s been a while since your math class days, fear not: There are handy tools for figuring out compounding. Many calculators (both handheld and computer-based) have exponent functions you can utilize for these purposes.

### Calculating Compound Interest in Excel

If more complicated compounding tasks arise, you can perform them in Microsoft Excel in three different ways:

1. The first way to calculate compound interest is to multiply each year’s new balance by the interest rate. Suppose you deposit \$1,000 into a savings account with a 5% interest rate that compounds annually, and you want to calculate the balance in five years. In Microsoft Excel, enter “Year” into cell A1 and “Balance” into cell B1. Enter years 0 to 5 into cells A2 through A7. The balance for year 0 is \$1,000, so you would enter “1000” into cell B2. Next, enter “=B2*1.05” into cell B3. Then enter “=B3*1.05” into cell B4 and continue to do this until you get to cell B7. In cell B7, the calculation is “=B6*1.05”. Finally, the calculated value in cell B7—\$1,276.28—is the balance in your savings account after five years. To find the compound interest value, subtract \$1,000 from \$1,276.28; this gives you a value of \$276.28.
2. The second way to calculate compound interest is to use a fixed formula. The compound interest formula is ((P*(1+i)^n) - P), where P is the principal, i is the annual interest rate, and n is the number of periods. Using the same information above, enter “Principal value” into cell A1 and “1000” into cell B1. Next, enter “Interest rate” into cell A2 and “.05” into cell B2. Enter “Compound periods” into cell A3 and “5” into cell B3. Now you can calculate the compound interest in cell B4 by entering “=(B1*(1+B2)^B3)-B1”, which gives you \$276.28.
3. A third way to calculate compound interest is to create a macro function. First start the Visual Basic Editor, which is located in the developer tab. Click the Insert menu, and click on “Module.” Then type “Function Compound_Interest (P As Double, I As Double, N As Double) As Double” in the first line. On the second line, hit the tab key and type in “Compound_Interest = (P*(1+i)^n) - P.” On the third line of the module, enter “End Function.” You have created a function macro to calculate the compound interest rate. Continuing from the same Excel worksheet above, enter “Compound interest” into cell A6 and enter “=Compound_Interest(B1, B2, B3).” This gives you a value of \$276.28, which is consistent with the first two values.

### Other Compound Interest Calculators

Several free compound interest calculators are offered online, and many handheld calculators can carry out these tasks as well:

• The free compound interest calculator offered through Financial-Calculators.com is simple to operate and offers to compound frequency choices from daily through annually. It includes an option to select continuous compounding and also allows input of actual calendar start and end dates. After inputting the necessary calculation data, the results show interest earned, future value, annual percentage yield (APY) (a measure that includes compounding), and daily interest.
• Investor.gov, a website operated by the U.S. Securities and Exchange Commission (SEC), offers a free online compound interest calculator. It is fairly simple and also allows inputs of monthly additional deposits to the principal, which helps calculate earnings when additional monthly savings are being deposited.
• A free online interest calculator with a few more features is available at TheCalculatorSite.com. This calculator allows calculations for different currencies, the ability to factor in monthly deposits or withdrawals, and the option to have inflation-adjusted increases to monthly deposits or withdrawals automatically calculated as well.

## How Can I Tell if Interest Is Compounded?

The Truth in Lending Act (TILA) requires that lenders disclose loan terms to potential borrowers, including the total dollar amount of interest to be repaid over the life of the loan and whether interest accrues simply or is compounded.

Another method is to compare a loan’s interest rate to its annual percentage rate (APR), which the TILA also requires lenders to disclose. The APR converts the finance charges of your loan, which include all interest and fees, to a simple interest rate. A substantial difference between the interest rate and APR means one or both of two scenarios: Your loan uses compound interest, or it includes hefty loan fees in addition to interest. Even when it comes to the same type of loan, the APR range can vary wildly among lenders depending on the financial institution’s fees and other costs.

You’ll note that the interest rate you are charged also depends on your credit. Loans offered to those with excellent credit carry significantly lower interest rates than those charged to borrowers with poor credit.

## What Is a Simple Definition of Compound Interest?

Compound interest simply means that the interest associated with a bank account, loan, or investment increases exponentially—rather than linearly—over time. The key word here is compound.

Suppose you make a \$100 investment in a business that pays you a 10% dividend every year. You have the choice of either pocketing those dividend payments like cash or reinvesting them into additional shares. If you choose the second option, reinvesting the dividends and compounding them together with your initial \$100 investment, then the returns you generate will start to grow over time.

## Who Benefits From Compound Interest?

Compound interest benefits investors, but the meaning of investors can be quite broad. Banks, for instance, benefit from compound interest when they lend money and reinvest the interest they receive into giving out additional loans. Depositors also benefit from compound interest when they receive interest on their bank accounts, bonds, or other investments.

It is important to note that although the term compound interest includes the word interest, the concept applies beyond situations for which the word is typically used, such as bank accounts and loans.

## Can Compound Interest Make You Rich?

Yes. Compound interest is arguably the most powerful force for generating wealth ever conceived. There are records of merchants, lenders, and various businesspeople using compound interest to become rich for literally thousands of years. In the ancient city of Babylon, for example, clay tablets were used more than 4,000 years ago to instruct students on the mathematics of compound interest.

In modern times, Warren Buffett became one of the richest people in the world through a business strategy that involved diligently and patiently compounding his investment returns over long periods. It is likely that, in one form or another, people will be using compound interest to generate wealth for the foreseeable future.

## The Bottom Line

The long-term effect of compound interest on savings and investments is indeed miraculous. Because it grows your money much faster than simple interest, it is a central factor in increasing wealth. It also mitigates a rising cost of living caused by inflation, as it will almost certainly outpace it.

For young people especially, compound interest is a godsend, as they have the most time ahead of them in which to save. Remember when choosing your investments that the number of compounding periods is just as important as the interest rate. Is there anyone who wouldn’t want to turn \$48,000 into \$1.17 million, even if it takes 40 years to do it?

Article Sources
Investopedia requires writers to use primary sources to support their work. These include white papers, government data, original reporting, and interviews with industry experts. We also reference original research from other reputable publishers where appropriate. You can learn more about the standards we follow in producing accurate, unbiased content in our editorial policy.
1. Internal Revenue Service. "Topic No. 403 Interest Received."

2. Internal Revenue Service. "Publication 550 (2021), Investment Income and Expenses."

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4. U.S. Securities and Exchange Commission, Investor. "Compound Interest Calculator."

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