Compound interest calculator
Compound interest means you earn interest on your interest. The formula is A = P × (1 + r/n)^(n × t). Enter your starting balance, monthly deposit, annual rate and number of years, and the calculator shows your ending balance, total contributions, interest earned and a year-by-year chart.
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Estimate only, not financial advice. Real returns vary from year to year, and this calculation ignores inflation, fees and taxes.
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The compound interest formula
Each period, interest is added to the balance and then earns interest itself. With no deposits:
\[ A = P \times \left( 1 + \dfrac{r}{n} \right)^{n \times t} \]
P is the starting balance, r the annual rate as a decimal, n the number of compounding periods per year (12 for monthly, 1 for annual) and t the years. With a monthly deposit D made at the end of each month and monthly compounding (\( i = \dfrac{r}{12} \), N = number of months):
\[ A = P \times (1 + i)^{N} + \dfrac{D \times ((1 + i)^{N} - 1)}{i} \]
The calculator runs month by month. For another compounding frequency it uses the equivalent monthly rate, \( \left( 1 + \dfrac{r}{n} \right)^{\dfrac{n}{12}} - 1 \).
Why time beats rate
Compounding speeds up the longer you wait. Here is $10,000 invested at 5% a year with monthly compounding and no deposits:
| Years | Ending balance | Interest earned |
|---|---|---|
| 10 | $16,470 | $6,470 |
| 20 | $27,126 | $17,126 |
| 30 | $44,677 | $34,677 |
The Rule of 72 gives a quick doubling time: divide 72 by the rate. At 6%, money doubles in about 12 years.
Monthly, annual or daily compounding
The more often interest is added, the higher the result, but the gap is small. For $10,000 at 5% for 10 years:
| Compounding | Ending balance |
|---|---|
| Annually | $16,289 |
| Monthly | $16,470 |
| Daily | $16,487 |
Check whether a quoted rate is a nominal rate or an APY. A 5% nominal rate compounded monthly equals a 5.12% APY.
3 real-life examples
$10,000 at 5% for 10 years
No deposits, monthly compounding: \( 10{,}000 \times \left( 1 + \dfrac{0.05}{12} \right)^{120} = \) $16,470.09, which is $6,470.09 of interest.
$300 a month for 25 years at 6%
You contribute 300 × 300 months = $90,000. The ending balance reaches $207,898, of which $117,898 is interest: interest outweighs your own deposits.
$5,000 plus $150 a month for 30 years at 7%
You put in \( \$5{,}000 + 150 \times 360 = \$59{,}000 \). After 30 years the balance is about $223,578, with $164,578 coming from interest.