How compound interest works
With compound interest you earn interest not only on the money you put in, but also on the interest already added to your balance. Over time the interest itself starts earning interest, so the balance grows faster and faster. The longer you leave the money and the more often interest is added, the stronger the effect.
Enter your initial investment, a monthly contribution, the annual interest rate, how often interest compounds and the number of years. This compound interest calculator shows the final balance, how much of it you deposited and how much is interest, with a chart and a schedule by year and month.
The compound interest formula
- Single deposit: FV = P × (1 + r / n)n × t, where P is the starting amount, r the annual rate, n the number of compounding periods a year and t the number of years.
- Continuous compounding: FV = P × er × t.
- With monthly contributions: FV = P × (1 + i)m + C × ((1 + i)m − 1) / i, where C is the monthly contribution, m the number of months and i the monthly rate, (1 + r / n)n / 12 − 1. Contributions at the beginning of each month are multiplied by (1 + i) once more.
- Annual percentage yield: APY = (1 + r / n)n − 1, the yearly growth after compounding.
Example
$10,000 invested at 7% compounded monthly, with $500 added at the end of every month, grows to $300,850.72 in 20 years. You deposit $130,000, so $170,850.72 is interest, more than everything you put in. Adding the money at the beginning of each month gives $302,370.09. Without the monthly contributions, the $10,000 alone grows to $40,387.39.
Compound interest by compounding frequency
$10,000 at 7% for 20 years, with no contributions:
| Compounding | Ending balance | APY |
|---|---|---|
| Annually | $38,696.84 | 7.000% |
| Semiannually | $39,592.60 | 7.122% |
| Quarterly | $40,063.92 | 7.186% |
| Monthly | $40,387.39 | 7.229% |
| Daily | $40,546.56 | 7.250% |
| Continuously | $40,552.00 | 7.251% |
More frequent compounding gives a slightly higher result, because interest starts earning interest sooner. The jump from yearly to monthly matters; from daily to continuous it is only a few dollars.
How the balance grows over time
$10,000 to start and $500 a month at 7%, compounded monthly:
| Years | Money put in | Interest | Balance |
|---|---|---|---|
| 5 | $40,000 | $9,973 | $49,973 |
| 10 | $70,000 | $36,639 | $106,639 |
| 15 | $100,000 | $86,971 | $186,971 |
| 20 | $130,000 | $170,851 | $300,851 |
| 25 | $160,000 | $302,290 | $462,290 |
| 30 | $190,000 | $501,150 | $691,150 |
| 40 | $250,000 | $1,225,521 | $1,475,521 |
From year 17 on, the interest is larger than all the money you deposited. That is why time is the most powerful part of the formula: years 21 to 30 add more to the balance than the first 20 years together.
Simple vs. compound interest
Simple interest is paid only on the original amount: $10,000 at 7% earns $14,000 in 20 years. With monthly compounding the same deposit earns $30,387, more than twice as much. The simple interest calculator works out the simple kind.
The rule of 72
Divide 72 by the annual rate to estimate how many years it takes to double your money with yearly compounding:
| Rate | Rule of 72 | Exact years |
|---|---|---|
| 2% | 36.0 | 35.0 |
| 4% | 18.0 | 17.7 |
| 6% | 12.0 | 11.9 |
| 7% | 10.3 | 10.2 |
| 8% | 9.0 | 9.0 |
| 10% | 7.2 | 7.3 |
| 12% | 6.0 | 6.1 |
Compound interest on debt
Compounding works against you when you borrow. Credit cards usually compound daily: a $5,000 balance at 24% APR grows to about $6,356 in a year if you pay nothing. The credit card calculator shows how long it takes to pay a balance off.
Tips for growing savings
- Start early. Time is the most powerful part of the formula.
- Contribute regularly, even small amounts, and at the start of the month when you can.
- Compare accounts by APY, since it already includes the compounding.
- Watch fees and taxes — they reduce the rate your money really earns. The interest calculator adds tax and inflation.
- Remember inflation. A 7% return with 3% inflation is about 4% in real terms.
To reach a target amount, use the investment calculator; for savings with contributions that rise each year, the savings calculator.