How Compound Interest Works (with Examples)

Simple vs compound interest

Simple interest is paid only on your original amount, the principal. Compound interest is paid on the principal plus all the interest already added — so each period grows a little faster than the last.

Put $1,000 in at 10% a year. Simple interest adds a flat $100 every year. Compound interest adds $100 the first year, $110 the second (10% of $1,100), $121 the third — small gaps that widen enormously over decades.

The formula

A = P x (1 + r / n) ^ (n x t), where P is the principal, r the annual rate, n how many times a year it compounds, and t the number of years. The interest earned is simply A - P.

Example: $5,000 at 6% compounded monthly for 10 years. Here r/n = 0.005 and n x t = 120, giving A = 5,000 x 1.005^120 = about $9,097 — roughly $4,097 of pure interest, with no extra deposits. The Compound Interest Calculator shows this instantly.

Why time matters more than rate

Because growth builds on itself, the balance barely moves in the early years and then accelerates. That is why starting sooner — even with small amounts — usually beats starting later with more: the extra compounding periods do the heavy lifting.

Compounding frequency

The same rate grows to slightly more the more often it compounds. $10,000 at 5% for 20 years reaches about $26,533 compounded yearly, $27,126 monthly, and $27,181 daily. The jump from yearly to monthly is meaningful; monthly to daily is tiny. This is why banks quote an APY, which folds the frequency into one comparable number.

Adding regular contributions

Most real saving is not one deposit but a little every month. Adding $200 a month to a $1,000 start at 7% for 25 years grows to roughly $167,700 — of which only about $61,000 is money you put in. Time, not a huge monthly amount, produces the rest. The Savings Goal Calculator plans around a target like this.

The Rule of 72

To estimate how long money takes to double, divide 72 by the interest rate. At 6% that is 72 / 6 = about 12 years; at 9%, about 8 years. It is an approximation, but a good one for rates between roughly 4% and 12% — handy for quick mental math.

It works against you too

Compounding is neutral: it grows debt just as happily as savings. Credit cards often compound daily at high rates, which is why a balance can cost more in interest than the original purchase. For debt, the lesson is the mirror image — pay early and often.