Compound Interest — The Arithmetic That Rewards Starting Early

Compound interest is interest calculated on the balance including previously earned interest. Simple interest pays on the original amount only; compound interest pays on the growing total. That one difference is the engine behind most long-horizon financial arithmetic.

The mechanism in numbers

At 5 percent compounded annually, 1,000 dollars becomes 1,050 after one year. Year two pays 5 percent on 1,050, not 1,000, giving 1,102.50. The extra 2.50 looks like rounding. Run it for 30 years and the balance is about 4,322 dollars, of which more than three quarters is growth, and most of that growth arrived in the later years. Compounding is back-loaded: the curve looks flat early and steep late, which is why the effect consistently surprises people who judge it by the first few years.

The rule of 72

A quick approximation: dividing 72 by the annual rate gives the approximate years to double. At 6 percent, about 12 years. At 3 percent, about 24. It is arithmetic shorthand, not a prediction about any real account, but it makes rate differences tangible: a rate twice as high halves the doubling time.

The same force in reverse

Compounding has no allegiance. A credit card at 24 percent compounds against the borrower with the same mechanics, which is why balances that only receive minimum payments grow so stubbornly, and why the payoff-method arithmetic leans on rates. On the savings side, the rate that actually compounds is the after-tax rate, which the free After-Tax Yield Calculator computes per state.

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Educational only. Not financial advice. Results not guaranteed. We are not financial advisors.