How to Calculate Compound Interest (With Examples)

Compound interest is the reason a modest amount of money can grow into a much larger sum over time. Unlike simple interest, which only earns on your original deposit, compound interest earns on your original deposit and on the interest that has already been added. In other words, your interest starts earning interest. This guide walks through the formula, explains what each part means, and shows you how to run the numbers yourself.

The Compound Interest Formula

The standard formula for compound interest is:

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

Here is what each variable stands for:

A is the final amount, including both your principal and the interest earned.
P is the principal, or the amount of money you start with.
r is the annual interest rate, written as a decimal. A 6% rate becomes 0.06.
n is the number of times interest is compounded per year (for example, 12 for monthly).
t is the number of years the money is invested or borrowed.

A Worked Example

Suppose you deposit 5,000 dollars at an annual rate of 6%, compounded monthly, and leave it untouched for 10 years. Plug the values in:

P = 5,000
r = 0.06
n = 12
t = 10

First, divide the rate by the number of periods: 0.06 divided by 12 equals 0.005. Add 1 to get 1.005. The exponent is n times t, or 12 times 10, which is 120. So you raise 1.005 to the 120th power, giving roughly 1.8194. Finally, multiply by the principal: 5,000 times 1.8194 comes to about 9,097 dollars. That means your money earned roughly 4,097 dollars in interest without you adding a single extra cent.

Why Compounding Frequency Matters

The value of n changes your result. The more often interest compounds, the more often you earn interest on interest. Using the same 5,000 dollars at 6% for 10 years:

Compounded annually (n = 1): about 8,954 dollars.
Compounded monthly (n = 12): about 9,097 dollars.
Compounded daily (n = 365): about 9,110 dollars.

The difference between annual and daily compounding here is modest, but it grows with larger balances, higher rates, and longer time horizons. This is also why you may see accounts advertise an annual percentage yield (APY), which reflects the effect of compounding rather than the plain stated rate.

Adding Regular Contributions

Most people do not just make one deposit and walk away. They add money on a regular schedule, and this dramatically changes the outcome. Each new contribution begins compounding from the day it lands, so consistent deposits build momentum over time.

Imagine that alongside your initial 5,000 dollars, you add 200 dollars every month for those same 10 years at 6% compounded monthly. Your contributions alone total 24,000 dollars, but with compounding the balance grows to roughly 41,900 dollars. The extra growth beyond your deposits comes entirely from interest doing its work on a steadily rising balance. The math for contributions is more involved than the basic formula, since each deposit compounds for a different length of time.

Let a Calculator Do the Heavy Lifting

Working these figures by hand is useful for understanding the mechanics, but it gets tedious quickly, especially once you factor in monthly contributions. A tool handles the arithmetic instantly and lets you experiment. Try the compound interest calculator to test different rates, timeframes, and deposit amounts, and see how small changes today can add up to a meaningful difference years from now.

Key Takeaways

Compound interest earns returns on both your principal and your accumulated interest.
The formula A = P(1 + r/n)^(nt) captures principal, rate, frequency, and time.
More frequent compounding and a longer time horizon both boost your total.
Regular contributions accelerate growth far beyond a single deposit.