What Is Compound Interest?

Compound interest (or compounding interest) is interest calculated on the initial principal, which also includes all of the accumulated interest of previous periods of a deposit or loan. Thought to have originated in 17th century Italy, 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.

Key Takeaways

  • Interest can be compounded on any given frequency schedule, from continuous to daily to annually.
  • When calculating compound interest, the number of compounding periods makes a significant difference.

The rate at which compound interest accrues depends on the frequency of compounding, such that the higher the number of compounding periods, the greater the compound interest. Thus, the amount of compound interest accrued on $100 compounded at 10% annually will be lower than that on $100 compounded at 5% semi-annually over the same time period. Since the interest-on-interest effect can generate increasingly positive returns based on the initial principal amount, it has sometimes been referred to as the "miracle of compound interest."


Understanding Compound Interest

Calculating Compound Interest

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.

What is Compound Interest?
Katie Kerpel {Copyright} Investopedia, 2019.

The formula for calculating compound interest is:


                              = [P (1 + i)n] – P

                              = P [(1 + i)n – 1]



Growth of Compound Interest

Using the above example, since compound interest also takes into consideration accumulated interest in previous periods, the interest amount is not the same for all three years, as it would be with simple interest. While the total interest payable over the three-year period of this loan is $1,576.25, the interest payable at the end of each year is shown in the table below.

Compounding Periods




Excel Compounding Calculation

If it's been a while since your math class days, fear not: There are handy tools to help figure compounding. Many calculators (both handheld and computer-based) have exponent functions that can be utilized for these purposes. If more complicated compounding tasks arise, they can be done using 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.

Using Other Calculators

As mentioned above, a number of 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), which is 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. The calculator is fairly simple, but it does allow inputs of monthly additional deposits to the principal, which is helpful for calculating earnings where 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.

The Frequency of Compounding



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're wanting to put money in and take it out the same day.


Time Value of Money Consideration


The formula for obtaining the future value (FV) and present value (PV) are as follows:



= $10,000 (1 + 0.05)3

= $10,000 (1.157625)

= $11,576.25


= $11,576.25 / (1 + 0.05)3

= $11,576.25 / 1.157625

= $10,000


The "Rule of 72" Consideration


As an example, an investment that has a 6% annual rate of return will double in 12 years.

An investment with an 8% annual rate of return will thus double in nine years.

Compound Annual Growth Rate (CAGR)


Let's say your investment portfolio has grown from $10,000 to $16,000 over five years; what is the CAGR? Essentially, this means that PV = -$10,000, FV = $16,000, nt = 5, so the variable “i” has to be calculated. Using a financial calculator or Excel, it can be shown that i = 9.86%.


CAGR Real-life Applications



Example 1: A risk-averse investor is happy with a modest 3% annual rate of return on her portfolio. Her present $100,000 portfolio would, therefore, grow to $180,611 after 20 years. In contrast, a risk-tolerant investor who expects an annual return of 6% on her portfolio would see $100,000 grow to $320,714 after 20 years.



  • CAGRs also crop up frequently in economic data. Here is an example: China’s per-capita GDP increased from $193 in 1980 to $6,091 in 2012. What is the annual growth in per-capita GDP over this 32-year period? The growth rate “i” in this case works out to be an impressive 11.4%.

Pros and Cons of Compounding

While the magic 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 total compound interest of $4,388 over one year or about $365 per month.

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



Compound Interest Investments

An investor who opts for a reinvestment plan 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, 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. Speaking of loans…

Telling if Interest 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.