Compound Interest Calculator
See how savings grow when interest earns interest. Adjust the deposit, rate and horizon to watch the projection update, then check the working step by step.
Monthly deposits stay monthly. We use an equivalent monthly growth rate; actual bank crediting and day-count rules may differ. Enter years in whole months, such as 1.5 for 18 months.
On-screen number pad
Step-by-step proofCheck by hand
How the balance grows
The solid line is the balance; the dashed line is what you deposited. The gap between them is compound growth — money you never paid in.
Year-by-year breakdown
| Year | Starting value | Deposits | Interest earned | Cumulative deposits | Ending balance |
|---|
How compound interest actually works
Simple interest pays you only on the money you originally put in. Compound interest pays you on your deposit and on the interest that deposit has already earned. Each period, the base that interest is calculated against gets slightly larger — so the growth curve bends upward rather than running in a straight line.
That bend is the whole point, and it is why time matters more than almost anything else. The last decade of a thirty-year investment typically produces more growth than the first two decades combined, because it is compounding on the largest balance.
The formula
m = 12t
A = P(1+i)^m + C × ((1+i)^m − 1)/i
Here P is the initial principal, C the monthly deposit, r the nominal annual rate as a decimal, n the quoted compounding frequency, and m the number of months. For deposits at the start of each month, multiply the deposit term by (1+i). At a zero rate, A = P + C × m. Whole-month horizons are supported; the last schedule row may cover less than a year.
Worked example
$10,000 at 8.5% compounded monthly for 15 years, with no contributions: r/n = 0.085 ÷ 12 = 0.0070833. n×t = 180 periods. A = 10,000 × (1.0070833)180 = $35,626.53. Add $500 a month and the contributions and their own growth bring the total to roughly $216,520 — most of which you never deposited.