How it works
Compound interest means you earn interest on your interest. Each period, the interest is added to the balance, and the next period’s interest is calculated on that larger amount. Over long periods this makes growth speed up.
The formulas
For a single amount with no deposits:
A = P × (1 + r ÷ n)n × tP is the starting amount, r the yearly rate (as a decimal), n the number of compounding periods per year and t the number of years. Regular monthly deposits D add the future value of a series:
FV = D × ((1 + i)m − 1) ÷ iwhere i is the monthly rate and m the number of months (deposits at the end of each month; deposits at the start of the month earn one extra month of interest).
Worked examples. 10,000 at 5% compounded yearly for 10 years grows to 10,000 × 1.0510 = 16,288.95. Depositing 100 at the end of every month for 10 years at 6% compounded monthly gives 16,387.93: 12,000 of deposits plus 4,387.93 of interest.
How this calculator works it out
The yearly rate is converted into the equivalent monthly rate for your compounding choice — for monthly compounding it is r ÷ 12; for yearly, quarterly or daily compounding it is (1 + r ÷ n)n ÷ 12 − 1 — and the balance is then calculated month by month and rounded to the cent only for display. This lets monthly deposits work with any compounding frequency and gives the same answers as the formulas above.
Inflation: what the money will really buy
If you enter an expected inflation rate, the final amount is also shown in today’s money: balance ÷ (1 + inflation)years. With 10% inflation, 10,000 in one year buys what about 9,090.91 buys today. If your interest rate is below inflation, your savings lose purchasing power even though the number grows.
The rule of 72
A quick mental check: divide 72 by the yearly rate to estimate how many years it takes to double your money. At 6%, about 12 years; at 9%, about 8 years.
Comparing with a loan? The loan calculator uses the same monthly rate maths in reverse. For Islamic savings, see the zakat calculator.