How compound interest works

Simple versus compound interest

With simple interest, you earn interest only on the original amount. With compound interest, interest is added to the balance, and from then on it earns interest too.

The formula

For a lump sum:

A = P × (1 + r ÷ n)^(n × t)

• P is the starting amount.
• r is the annual rate as a decimal (5% = 0.05).
• n is how many times interest compounds per year.
• t is the number of years.

A worked example

Start with 10,000 at 5% a year, compounded annually, for 10 years:

10,000 × 1.05^10 ≈ 16,288.95

Simple interest on the same amount would give 10,000 + 10,000 × 0.05 × 10 = 15,000. The extra 1,288.95 is the effect of compounding.

What affects growth

• Time matters most: the longer the period, the larger the compounding effect.
• Rate: a higher rate compounds faster, but real returns are not guaranteed.
• Contributions: adding money regularly increases the balance that earns interest.
• Frequency: more frequent compounding gives slightly more growth.

Limits of any calculator

Calculators apply the rate you enter. They ignore taxes, fees and inflation, and real investments do not earn a fixed rate. Treat the output as an illustration, not a forecast or advice.

Try it with the Compound Interest Calculator.