How Compound Interest Works (and Why Time Beats Amount)

The basic idea

Simple interest is paid only on your original deposit. Compound interest is paid on the deposit plus all the interest already earned — so your balance grows a little faster every period, and the curve bends upward over time.

With $1,000 at 5% for 10 years, simple interest gives you $1,500. Compounded yearly you get $1,628.89. The extra $128.89 is interest earned on interest — small here, but over 30–40 years of retirement saving it becomes the largest part of the balance.

The formula

A = P(1 + r/n)^(nt), where P is the principal, r the annual rate as a decimal, n how many times interest compounds per year, and t the years. Regular contributions add a second term: each deposit compounds for the time it is invested.

Try it with your own numbers in the Compound Interest Calculator, and use the Savings Calculator to add a monthly deposit.

The Rule of 72

Divide 72 by the annual return to estimate how many years money takes to double. At 6%, about 12 years; at 9%, about 8 years. The same rule works backwards for inflation: at 4% inflation, prices double in roughly 18 years.

Frequency matters less than time

Daily compounding beats yearly compounding, but only slightly — at 5% for 10 years the difference on $10,000 is about $80. Starting five years earlier is worth far more than any change in compounding frequency.