Compound interest explained with real numbers

The formula

With a starting amount P, annual rate r compounded n times a year, the balance after t years is P × (1 + r/n)^(n·t). Regular monthly saving is added on top: each deposit then compounds for the months that remain.

Example: $500 a month at 7%

Saving $500 a month for 20 years at a steady 7% grows to about $260,463, of which $120,000 is your own money. Keep going for 30 years and it becomes about $609,985 — the extra 10 years add about $349,522 while you put in only $60,000 more. Starting with $10,000 as well gives about $300,851 after 20 years.

Time beats compounding frequency

$10,000 at 7% for 10 years grows to about $19,672 with yearly compounding, $20,097 with monthly and $20,136 with daily compounding. The difference between monthly and daily is tiny next to the effect of a few more years or one percentage point of return.

The rule of 72

Divide 72 by the annual rate to estimate how many years it takes to double: at 7%, about 10.3 years. The $10,000 above almost doubles in 10 years, as the rule predicts. It is a quick check, not an exact result.

What the calculator leaves out

Real returns are not a steady 7%: markets go up and down, and a bad year near the end matters more than one at the start. Taxes, fund fees and inflation also reduce the result. Use the calculator to compare plans, and treat the numbers as estimates, not promises.

Tools used in this guide