Compound Interest Calculator

How compound interest works

With simple interest you earn a fixed percentage of your original deposit every year. With compound interest the interest is added to the balance, and from then on it earns interest too. Over a few years the difference is small; over decades it becomes the larger part of the balance. In the default example — 10,000 to start, 200 added each month, 7% a year compounded monthly for 10 years — you put in 34,000 and end with about 54,713.58, so roughly 20,700 comes from interest.

For a single deposit with no further contributions, the classic formula is:

A = P × (1 + r/n)^(n × t)

where A is the future value, P the starting amount (the principal), r the annual rate as a decimal, n the number of compounding periods per year and t the number of years. 10,000 at 5% for 10 years grows to 16,288.95 with annual compounding and 16,486.65 with daily compounding.

The Rule of 72

A quick way to estimate how long money takes to double is to divide 72 by the yearly rate in percent. At 7% that gives 72 ÷ 7 ≈ 10.3 years; the exact figure with annual compounding is 10.24 years. At 4% it takes about 18 years. The rule is closest for rates between roughly 4% and 12%.

Monthly contributions with any compounding frequency

Regular deposits make the closed formula awkward, especially when deposits are monthly but interest compounds quarterly or daily. This calculator therefore simulates the account month by month. For each month it uses the monthly rate that is equivalent to the compounding you chose:

monthly rate = (1 + r/n)^(n/12) − 1

With monthly compounding (n = 12) this is just r/12. With annual compounding at 7% it is about 0.565% a month; twelve such months compound to exactly 7% for the year. With daily compounding (n = 365) it is about 0.585% a month. Each month the balance grows by that rate, then the monthly contribution is added at the end of the month.

One simplification is worth knowing. A real account with, say, quarterly compounding credits interest only at the end of each quarter, and money deposited partway through a quarter may earn simple interest or nothing until then. The effective-rate method spreads the growth evenly across the months instead. The totals at each compounding date match the bank’s formula for a lump sum, and for regular deposits the difference is usually a fraction of a percent.

Reading the chart and the table

Each bar in the chart is the balance at the end of a year. The lower part is money you contributed (your starting deposit plus all monthly deposits so far), the upper part is interest earned so far. In the early years the bars are mostly contributions. As time passes the interest part grows faster than the contribution part, which is the compounding effect you can see without reading any numbers. The table underneath lists the exact figures for every year.

Tips for using the results

• Try changing one input at a time. Adding five years usually has a bigger effect than adding a percentage point to the rate.
• Compare a scenario with a higher starting deposit and lower contributions against the reverse to see which suits your budget.
• Use realistic rates. High-yield savings accounts and certificates of deposit publish their rates; long-term stock returns are averages, not guarantees.
• For a deposit with a fixed term, such as an 18-month CD, the date calculator gives the exact maturity date.
• Remember that inflation reduces what the final amount can buy, so look at the result in today’s money as well.