How Compound Interest Works, With Worked Examples

Compound interest means earning interest not only on the money you put in, but also on the interest that money has already earned. Over short periods the effect is small. Over decades it becomes the dominant force in long-term saving, and in long-term debt.

Simple vs compound interest

With simple interest, you earn interest only on the original amount. 10,000 at 7% simple interest earns 700 every year, so after 10 years you have 17,000.

With compound interest, each year's interest is added to the balance and earns interest itself. 10,000 growing at 7% a year, compounded annually, becomes about 19,672 after 10 years. The difference, 2,672, is interest on interest.

The formula

Future value = Principal × (1 + r)ⁿ, where r is the rate per period and n is the number of periods.

Continuing the example at 7% a year:

The money roughly doubles every ten years, so the largest gains come at the end. That is why time matters more than almost anything else.

The Rule of 72

To estimate how long money takes to double, divide 72 by the annual rate. At 6%, about 12 years; at 9%, about 8 years. It is an approximation, but a remarkably good one for typical rates, and it works for inflation too: at 4% inflation, prices roughly double in 18 years.

Starting ten years earlier

Consider two savers who each put 200 a month into an account growing at 6% a year, compounded monthly:

• Saver A starts at 25 and continues for 30 years. Total contributed: 72,000. Value at 55: about 200,900.
• Saver B starts at 35 and continues for 20 years. Total contributed: 48,000. Value at 55: about 92,400.

Saver A contributed 24,000 more but ended with roughly 108,000 more. Most of the difference is compounding on the early contributions. These are illustrative calculations with a constant return; real investments fluctuate and are not guaranteed.

Compounding frequency

Interest can compound yearly, monthly or daily. More frequent compounding produces a slightly higher result at the same headline rate. That is why savings products quote an annual equivalent rate (AER or APY) and loans quote an annual percentage rate (APR): they let you compare products on a like-for-like basis.

The other side: debt

Compounding works against you when you borrow. Credit card balances that are not paid in full accumulate interest on interest, often at high rates. Paying only the minimum can mean a balance takes many years to clear and costs far more than the original purchases. If you have expensive debt, paying it down is often the best "investment" available; our comparison of debt repayment methods explains how to prioritise.

What reduces compounding

• Fees: a 1% annual fee compounds too, and can take a large share of long-term growth.
• Inflation: what matters is growth above inflation.
• Withdrawals: taking money out early removes the base that future growth builds on.
• Taxes: tax-advantaged accounts available in your country can help returns compound for longer.

Try your own numbers

The U.S. SEC's investor education site offers a free compound interest calculator where you can change the starting amount, monthly contribution, rate and time period. Try adding five years, or 50 more per month, and watch what changes.

This article is educational and is not investment advice. Investments can fall as well as rise.