Compound Interest: How Growth Actually Stacks

Compound interest means each period earns interest on the growing balance, not just on the starting amount. Adding 5% ten separate times understates the result.

The core idea

Simple interest adds a fixed slice of the original principal each year. Compound interest multiplies the current balance by (1 + rate) each year, so the interest itself earns interest.

Annual compounding formula: A = P × (1 + r)ⁿ, where P is the starting amount, r is the decimal rate per year, and n is the number of years.

Worked example

Start with $1,000 at 5% per year for 10 years, compounded once a year.

1. Rate as a decimal: r = 0.05, so the growth factor is 1.05.
2. Raise to 10 years: compute 1.05^10.
3. Multiply by the principal: 1,000 × 1.05^10 = $1,628.89 (rounded to cents).

Check on the scientific calculator: type 1000 × 1.05^10.

Rule of 72 (quick estimate)

A rough doubling time in years is 72 ÷ (percent rate). At 6%, that is about 72 ÷ 6 = 12 years. The exact figure for continuous annual compounding at 6% is close to 11.9 years, so the shortcut is useful for estimates—not for bank contracts.

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Related CalcSolver reading

Percent language still matters for rates and discounts—see Percent problems: 5 traps to avoid and the Percent Calculator.