Compound Interest Calculator

The formula, and why this page simulates monthly

The textbook version of compound interest fits on one line. In the formula below, P is the initial deposit, PMT is the monthly contribution, r is the nominal annual rate, n is the number of compounding periods per year and t is the time in years.

Rather than evaluate that closed form once, this calculator walks the balance forward month by month, so each contribution lands exactly where a real paycheck would and starts earning the moment it arrives. A worked example: start with $10,000, add $500 every month at 7% for 10 years and the balance reaches about $106,639. Of that, $70,000 came from you and $36,639 is interest the money earned by itself.

APR versus APY: the frequency dividend

The rate an account advertises and the rate your balance actually experiences are not the same number once interest compounds more than once a year. The advertised figure is the APR; the realized figure is the APY, and the gap between them is the frequency dividend.

In balances: $10,000 at 5% for 10 years compounds to $16,289 with annual compounding, $16,470 with monthly and $16,487 with daily. Frequency is free money, but note its size: roughly $200 over a decade. Time and rate move balances far more than switching institutions for a better compounding schedule.

Time is the loudest lever

Compounding is exponential, so the final years of a plan produce more growth than the early ones combined. Two savers each contributing $500 a month at 7% write the same checks; the one who starts at 25 instead of 35 reaches 55 with roughly $610,000 against $260,000, more than double the balance for the same outlay. Ten extra years did that work.

For mental math, use the Rule of 72: divide 72 by the annual rate to estimate how long money takes to double.

Run your own numbers

1. Set the initial deposit, the money you already have. Enter 0 if you are starting from nothing.
2. Set the monthly contribution. Set it to 0 to project a single lump sum.
3. Pick the annual interest rate; 7% is a defensible long-run nominal figure for globally diversified equities.
4. Choose the compounding frequency and the contribution timing. Most accounts compound daily or monthly, and start-of-month timing buys each deposit a few extra weeks of growth.
5. Set the years to grow, read the future value and the split between deposits and interest, then sweep the frequency slider to watch the APY move.

Compounding answers how money grows, not how much you need. To reverse the question and solve for the contribution a target requires, use the savings goal calculator. For the long horizon, where the schedule of contributions matters less than staying invested, the FIRE calculator models decades with inflation included. And keep returns honest: they are nominal, so at 2.5% inflation a 7% nominal return spends like roughly 4.5% in real purchasing power. For the debt side of the same arithmetic, see the loan payoff and amortization calculator.