Compound interest is interest earned on both the initial principal and previously accumulated interest. Unlike simple interest, which only earns on the original amount, compound interest grows exponentially. Einstein reportedly called it the eighth wonder of the world.
The compound interest formula
The standard formula calculates the future value of an investment:
A = P(1 + r/n)^(nt)
Where:
- A = future value
- P = principal (initial investment)
- r = annual interest rate (as a decimal)
- n = number of times interest compounds per year
- t = number of years
Worked example: $10,000 at 7% compounded monthly for 10 years. Monthly rate: 0.07 ÷ 12 = 0.005833. Total periods: 12 × 10 = 120. Growth factor: (1.005833)^120 ≈ 2.0097. Future value: 10000 × 2.0097 ≈ $20,097. That is $10,097 in interest earned. Try it on our interactive Interest Calculator, explore the compound interest calculator, or read our simple vs compound interest guide.
The rule of 72
A quick way to estimate how long it takes to double your money: divide 72 by the interest rate. At 7%, it takes about 72 ÷ 7 ≈ 10.3 years. At 10%, about 7.2 years. This works because of the same exponential growth.
Compounding frequency matters
The more often interest compounds, the higher the effective return:
| Frequency | Periods/year | Effective rate (at 7%) |
|---|---|---|
| Annual | 1 | 7.000% |
| Semi-annual | 2 | 7.122% |
| Quarterly | 4 | 7.186% |
| Monthly | 12 | 7.229% |
| Daily | 365 | 7.250% |
The difference between monthly and daily compounding is only 0.021%, but on large sums over decades, it adds up.
Regular contributions accelerate growth
Adding even small amounts regularly makes a dramatic difference. Investing $200 per month at 7% for 10 years on top of a $10,000 initial investment grows to approximately $47,500 — more than doubling what you would get from the initial investment alone.
Compound interest works against you too
Credit cards and loans with compound interest mean you owe interest on previously charged interest. A $5,000 credit card balance at 20% APR, making only minimum payments, can take decades to pay off and cost thousands in interest. Use the percentage calculator to understand the rate impact, and the average guide to understand how typical returns are calculated.
Frequently asked questions
How often is interest compounded? Common compounding frequencies are annual (1x), semi-annual (2x), quarterly (4x), monthly (12x), and daily (365x). More frequent compounding results in slightly higher returns.
What is the rule of 72? The rule of 72 estimates how long it takes for an investment to double: divide 72 by the interest rate. At 7%, it takes about 72/7 ≈ 10.3 years to double.
Is compound interest always better than simple interest? For investments, yes — compound interest grows faster. For loans, compound interest means you pay more over time, so simple interest loans are cheaper.
What is continuous compounding? Continuous compounding applies interest at every instant. The formula is A = Pe^(rt), where e ≈ 2.71828. It produces the maximum possible growth for a given rate.