How to use the compound interest calculator
- Enter the Initial deposit (it can be zero) and the Monthly contribution you plan to add.
- Enter the Interest rate (% per year) – a savings rate or an expected average return – and the number of Years, from 1 to 100.
- Choose how often interest is compounded: yearly, twice a year, quarterly, monthly or daily.
- Read the final balance and how much of it you paid in and how much is interest. The chart stacks deposits and interest for each year, and the table lists the deposits, the interest earned that year, the total interest and the balance.
How the calculation works
Compound interest means interest is added to the balance and then earns interest itself. For a single deposit the classic formula is A = P × (1 + r/n)^(n × t), where P is the starting amount, r the annual rate, n the number of compounding periods per year and t the number of years.
Because contributions are monthly, the calculator turns the chosen compounding into an equivalent monthly rate, (1 + r/n)^(n/12) − 1, and applies it every month. Contributions are added at the end of each month and start earning the month after. With no contributions, the result matches the formula above exactly.
Worked examples
- The starting values: 10,000 plus 200 a month at 5% for 10 years, compounded monthly, grows to 47,526.55. You paid in 34,000, so 13,526.55 is interest. The interest earned in year 10 alone (2,249.45) is about four times that of year 1 (567.39).
- Compounding frequency: 10,000 at 5% for 10 years with no contributions becomes 16,288.95 with yearly compounding, 16,470.09 monthly and 16,486.65 daily. More frequent compounding helps, but the step from monthly to daily is small.
- Starting early: at 6%, saving 200 a month for 30 years and 400 a month for 15 years both mean 72,000 of deposits. The first ends with 200,903.01, the second with 116,327.48 – fifteen extra years of compounding are worth more than doubling the contributions.
- Trying a range: the starting values give 41,441.82 at 3% and 54,713.58 at 7%. When returns are uncertain, a low and a high scenario are more honest than a single number.
Nominal rate and effective yield (APY)
A rate of 5% compounded monthly actually earns about 5.12% over a year; quarterly compounding gives about 5.09% and daily about 5.13%. This effective rate is called the APY (annual percentage yield) or AER. If your bank quotes an APY or AER, enter that figure and choose Yearly compounding – the calculator then reproduces the bank's effective growth, monthly contributions included.
The rule of 72
To estimate how long it takes to double your money, divide 72 by the annual rate in percent. At 6% that is 72 ÷ 6 = 12 years (the exact figure with yearly compounding is 11.9); at 9% about 8 years; at 3% about 24. The rule is close for typical rates up to about 12%, and it works for anything that grows by a steady percentage: with 3% inflation, prices double in roughly 24 years.
Tips and common mistakes
- Think in today's money. Inflation reduces what the final balance can buy. Entering a real rate – roughly the return minus inflation, such as 5% − 2% ≈ 3% – shows the result in today's purchasing power.
- Include taxes and fees. Tax on interest and account or fund fees lower the effective rate, so lower the rate you enter to match.
- Investment returns aren't fixed. Shares may average a certain return over long periods but rise and fall from year to year. The calculator uses the same rate every year, so the result is a scenario, not a forecast.
- Check whether a product pays simple interest. Some fixed-term deposits pay interest only on the original amount, and grow more slowly than shown here.
- Negative rates are accepted, which can show the effect of steady losses or fees larger than the return.
FAQ
Are contributions added at the start or the end of the month?
At the end. If you pay in at the start of each month, your real result will be slightly higher.
Why doesn't my bank statement match exactly?
Banks may compound daily, credit interest on fixed dates, round each month or deduct tax before paying interest. Small differences are normal.
Can I model a yearly contribution?
Approximately: divide it by 12 and enter it as a monthly contribution. The result will be a little higher than paying the whole amount once at the end of each year.
How is this related to loans?
A loan is compound interest working against you. The Loan Calculator shows how a balance is paid down over time, and the Percentage Calculator handles quick percentage changes.
The results are estimates based on a constant rate. They are not financial advice or a promise of future returns.