Compound Interest Calculator

How compound interest works

Compound interest is interest paid on your original money and on the interest it has already earned. Each time interest is credited, the balance gets bigger, so the next round of interest is calculated on a bigger number. With simple interest, by contrast, you earn the same dollar amount every year because interest is only ever paid on the original deposit.

The effect is slow at first and then speeds up. In the default example above, interest is a small slice of the balance in the early years, but by year 20 it makes up more than half of it. That is why starting early tends to matter more than finding a slightly higher rate.

What changes the answer most

Time and rate dominate. Doubling the number of years more than doubles the interest, because the later years compound on everything that came before. A rough guide is the rule of 72: divide 72 by the annual rate to estimate how many years it takes money to double. At 7%, that is about 10.3 years; the exact answer is 10.24 years.

Compounding frequency matters less than people expect. $10,000 at 7% for 10 years grows to $19,671.51 with yearly compounding, $20,096.61 with monthly compounding and $20,136.18 with daily compounding. Continuous compounding, the mathematical limit, adds only about another $1.35.

Contribution timing makes a small, steady difference. Money added at the start of each period earns one extra period of interest, so it always ends slightly ahead of the same contributions made at the end.

Using the result

Use a rate that matches what you are modeling. Savings accounts and CDs quote a known rate. Stock and bond investments have no fixed rate, so any figure you enter is an assumption, and real returns arrive unevenly, with losing years mixed in. Try a lower rate as well as your expected one to see a cautious case.

The result is in future dollars. Inflation means a balance 20 years from now will buy less than the same amount today; the investment calculator can show the figure in today's dollars. Interest in a regular taxable account is also taxed each year, which slows growth compared with a tax-advantaged account such as an IRA or 401(k).

The compound interest formula

• P = initial amount, C = contribution each period
• r = annual interest rate as a decimal, n = compounding periods per year, t = years
• i = interest rate per contribution period = (1 + r ÷ n)^(n ÷ periods per year) − 1
• N = total number of contributions (periods per year × years)

Example

1. You invest $10,000, add $200 at the end of every month, and earn 7% compounded monthly for 20 years.
2. Monthly rate i = 0.07 ÷ 12 = 0.5833%. Number of months N = 240.
3. The initial $10,000 grows to 10,000 × 1.005833^240 = $40,387.39.
4. The contributions grow to 200 × (1.005833^240 − 1) ÷ 0.005833 = $104,185.33.
5. Final balance: $144,572.72. You put in $58,000 in total, so $86,572.72 is interest.
6. If you made each contribution at the start of the month instead, the balance would be $145,180.47.

Frequently asked questions