Compound Interest — The 8th Wonder

What is compound interest?

Simple interest pays you on your original money only. Compound interest pays you on your original money plus the interest you’ve already earned. That’s the magic — your interest starts earning interest.

The formula

The value of an investment after n periods is:

A = P × (1 + r)ⁿ

• P = starting amount (principal)
• r = interest rate per period (as a decimal)
• n = number of periods

Why time beats amount

Two people can invest the same total, but the one who starts earlier ends up far richer. This is the “snowball” effect. A small amount invested at 16 can outgrow a large amount invested at 30.

Albert Einstein reportedly called compound interest “the eighth wonder of the world. He who understands it, earns it; he who doesn’t, pays it.”

The Rule of 72

Want a quick estimate of how long money takes to double? Divide 72 by the annual interest rate.

• At 6% a year: 72 ÷ 6 = 12 years to double.
• At 9% a year: 72 ÷ 9 = 8 years to double.

Try it yourself

Use the calculator on this page. Change the starting amount, monthly contribution, and rate — then watch the curve bend upward. That bend is compounding at work.

Key takeaways

• Compound interest pays interest on interest.
• A = P × (1 + r)ⁿ is the core formula.
• Starting early beats starting big.
• The Rule of 72 estimates doubling time.