Compound Interest Calculator Guide: The Formula, Explained
The compound interest formula broken down piece by piece, with a full worked example and a direct comparison against simple interest.
Compound interest is the mechanism behind almost every long-term savings and investment projection — understanding the formula makes it obvious why time matters so much more than most people expect.
The formula
A = P(1 + r/n)nt — where A is the future value, P is the principal, r is the annual interest rate as a decimal, n is the number of times interest compounds per year, and t is the time in years.
Worked example
$10,000 invested at 7% annual interest, compounded annually, for 20 years: A = 10,000 × (1.07)20 = $38,696.84.
Compound vs. simple interest, side by side
| Years | Simple interest total | Compound interest total |
|---|---|---|
| 10 | $17,000.00 | $19,671.51 |
| 20 | $24,000.00 | $38,696.84 |
| 30 | $31,000.00 | $76,122.55 |
The gap between simple and compound interest widens dramatically over time — at 30 years, compound interest produces nearly 2.5× the simple interest total on the same $10,000 principal and 7% rate, purely because compound interest earns returns on its own prior returns.
Model your own principal, rate, and time in the Compound Interest Calculator, including optional monthly contributions.