How Compound Interest Works
7 min read · Updated September 26, 2026 · by the SolveCalcPro editorial team
Compound interest is interest earned on both your original money and on the interest it has already earned. It is why savings can grow slowly at first and then much faster, and why debt can spiral if left alone. This guide explains the formula and shows the numbers.
Simple versus compound interest
Simple interest pays a fixed amount on the original principal each year. Compound interest recalculates on the growing balance. Here is $10,000 at 7% a year (compounded monthly for the last column):
| Years | Simple interest | Compound (monthly) |
|---|---|---|
| 10 | $17,000 | $20,097 |
| 20 | $24,000 | $40,387 |
| 30 | $31,000 | $81,165 |
After 30 years compounding earns more than double the simple interest.
The formula
A = P(1 + r/n)nt where P is the principal, r the annual rate as a decimal, n the number of compounding periods per year and t the number of years. For $10,000 at 7% compounded monthly for 10 years: A = 10,000 × (1 + 0.07/12)120 = $20,096.61. Use the compound interest calculator to try your own numbers.
Adding regular contributions
Regular deposits make a big difference. Starting with $10,000 and adding $200 a month at 7% compounded monthly for 20 years grows to about $144,573. You paid in $58,000, so about $86,573 came from interest, which is more than you put in yourself.
The Rule of 72
To estimate how long money takes to double, divide 72 by the annual rate. At 8% that is 72 ÷ 8 = 9 years. The exact figure is ln 2 ÷ ln 1.08 ≈ 9.006 years, so $1,000 becomes about $1,999 in 9 years. At 6% it takes about 12 years, and at 3% about 24 years.
Frequency matters less than time and rate
Compounding daily instead of yearly adds only a little. Adding years or a slightly higher rate matters much more. Starting ten years earlier usually beats saving more later.
Compounding works against debt too
Credit cards compound interest on unpaid balances, often at 20% or more. A balance that only receives minimum payments can take years to clear and cost far more than the original purchase. Paying down high-interest debt is often the best guaranteed return available.
What the formula leaves out
Real returns vary from year to year, and inflation, taxes and fees reduce what you keep. Treat projections as estimates, not promises. This page is educational and is not financial advice.
Practice questions
Test yourself, then tap to check. Answers are calculated by the tools linked below.
- $5,000 at 5% compounded yearly for 15 years, no contributions.
Show answer
Future value: $10,394.64
- What interest does $8,000 earn at 3.5% over 4 years?
Show answer
Interest earned: $1,120.00
- Calculate 7^4.
Show answer
7^4: 2,401
Frequently asked questions
What is compound interest in simple words?
Interest on interest. Each period’s interest is added to the balance, and the next period earns interest on the bigger balance.
Is daily compounding much better than yearly?
Slightly. At 7%, $10,000 for 10 years is about $19,672 with yearly compounding and about $20,096 with monthly, a small difference compared with the time invested.
How do I calculate compound interest by hand?
Multiply the principal by (1 + r/n) once for each compounding period. For yearly compounding, that is P × (1 + r) repeated t times.
What is APY?
Annual percentage yield is the effective yearly rate after compounding is included, so it is slightly higher than the stated rate.
Try it yourself
Compound Interest CalculatorSee how savings grow with compounding and regular contributions.Simple Interest CalculatorCalculate interest earned or owed with I = P × r × t.
Exponent CalculatorRaise any number to a power, including negative and fractional exponents.Keep learning
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