How to Calculate Compound Interest Step by Step
A clear step-by-step guide to calculating compound interest manually, with a simple formula breakdown and real-world examples.
What Is Compound Interest
Compound interest is interest calculated on both the original principal and the accumulated interest from previous periods. In simpler terms, you earn interest on your interest, which causes money to grow faster than simple interest over time.
It shows up everywhere in personal finance. Savings accounts, investment accounts, retirement funds, and most bonds use compounding. So do credit cards, most mortgages, and many loans — except in those cases, the compounding works against you instead of for you.
Understanding how to calculate it gives you the ability to estimate how much a savings account will grow, how much debt will balloon if left unpaid, and whether a financial product is offering you a good deal.
The Formula Made Simple
The standard compound interest formula is A = P times (1 + r divided by n) raised to the power of (n times t). Each letter stands for a specific value. A is the final amount of money you end up with. P is the principal, meaning the starting amount. R is the annual interest rate expressed as a decimal. N is the number of times interest compounds per year. T is the number of years.
That looks complicated written out, but the calculation is straightforward once you plug in real numbers. Most people use a calculator or spreadsheet for the math itself. What matters is understanding what each variable means so you can use the formula correctly.
Compounding frequency is the variable most people overlook. If interest compounds monthly (n equals 12), your money grows slightly faster than if it compounds annually (n equals 1). Daily compounding (n equals 365) is fastest. Most savings accounts compound daily or monthly.
Step 1 - Identify Your Variables
Start by writing down your four input values. Say you invest $5,000 in an account that earns 6% annual interest, compounded monthly, and you plan to leave it for 10 years.
Your principal P is $5,000. Your annual rate r is 6%, which you convert to 0.06 by dividing by 100. Your compounding frequency n is 12 because interest compounds monthly. Your time t is 10 years.
Getting these values right is the entire job. The math that follows is just arithmetic. If you are looking at a bank account, the interest rate and compounding frequency are on the product disclosure. If you are analyzing a loan, these figures are in the loan agreement.
Step 2 - Apply the Formula
With P equals 5000, r equals 0.06, n equals 12, and t equals 10, the calculation works like this. First, divide the rate by the compounding frequency: 0.06 divided by 12 equals 0.005. Then add 1: 1 plus 0.005 equals 1.005.
Next, calculate the exponent by multiplying n times t: 12 times 10 equals 120. Raise 1.005 to the power of 120. A calculator gives you approximately 1.8194. Finally, multiply that by your principal: 5000 times 1.8194 gives you approximately $9,097.
So your $5,000 investment grows to about $9,097 after 10 years at 6% compounded monthly. The total interest earned is $9,097 minus $5,000, which equals roughly $4,097. You have nearly doubled your money without adding a single extra dollar.
Real-World Examples
Example one: you put $2,000 in a high-yield savings account at 4.5% APY compounded daily for 3 years. Using the formula, you end up with about $2,288. The $288 earned is small but completely passive — no work required.
Example two: you carry a $3,500 credit card balance at 22% APR compounded daily and make no payments for one year. After 12 months, the balance has grown to roughly $4,278. That is $778 in interest charges for doing nothing. This example illustrates why paying off high-interest debt quickly matters so much.
Example three: a retirement account with $10,000 invested at age 30, earning 7% compounded annually for 35 years. By age 65, that single $10,000 deposit grows to approximately $106,766. Compound interest over long time horizons produces numbers that are genuinely hard to believe until you run the calculation yourself.