Compound interest formula
Compound interest grows money faster than simple interest because each period earns interest on the interest already added. This formula gives the final balance from the principal, rate, compounding frequency, and time.
- A = the final amount, including interest
- P = the principal, the starting amount
- r = the annual interest rate, as a decimal
- n = the number of times interest compounds per year
- t = the time in years
Why compounding matters
With simple interest, only the original principal earns interest. With compound interest, the interest itself starts earning interest, so the balance grows faster and faster over time. The more often it compounds, monthly rather than yearly for example, the more the effect adds up, though the extra gain from increasing frequency shrinks at the extremes.
Reading the formula
The rate is divided by n to get the rate per compounding period, and the exponent n times t counts the total number of periods. Raising one plus the periodic rate to that power gives the total growth factor, which multiplies the principal to give the final amount. The interest earned is simply A minus P.
- Start with P = 1000 dollars, r = 0.05 (5 percent), n = 12 (monthly), t = 10 years.
- Periodic rate: 0.05 / 12 = 0.004167.
- Number of periods: 12 × 10 = 120.
- A = 1000 × (1.004167)120 ≈ 1647.01 dollars, so the interest earned is about 647 dollars.
Run the numbers
Use the Compound Interest Calculator to project any balance over time.
FAQ
What is the difference between simple and compound interest?
Simple interest is earned only on the principal; compound interest is earned on the principal plus previously added interest, so it grows faster.
What does compounding frequency change?
More frequent compounding (monthly versus yearly) produces slightly more interest, because interest is added and starts earning sooner.