How does compound interest work?
Short answer
Compound interest is interest earned on both the original amount and the interest already added. Over time it grows faster than simple interest, which is paid only on the original amount.
Simple versus compound
Simple interest is calculated only on the principal. Compound interest is added to the balance at each compounding period, so the next period’s interest is calculated on a larger amount.
Simple: A = P x (1 + r x t)
Compound: A = P x (1 + r / n)^(n x t)
P = principal, r = annual rate (decimal), n = compounding periods per year, t = yearsA worked example
Illustrative arithmetic at an assumed rate: 1,000 at 8% a year compounded annually for 10 years becomes 1,000 x 1.08^10 = about 2,158.92. With simple interest the same sum would reach 1,000 x (1 + 0.08 x 10) = 1,800. The difference is interest earning interest.
More frequent compounding, such as monthly rather than annually, gives a slightly higher result at the same stated rate. The annual percentage yield (APY) or effective annual rate expresses the combined effect in one figure.
The rule of 72
A quick estimate of how long money takes to double is 72 divided by the annual rate in percent. At 8%, 72 / 8 = 9 years, which is close to the exact answer of about 9.01 years. It is a rough approximation that works best for rates between about 6% and 10%.
Years to double (approx.) = 72 / annual rate (%)It works against borrowers too
Interest on debts such as credit cards also compounds, so unpaid balances grow. Reading whether a rate is simple or compound, and how often it compounds, is part of comparing deposits and loans.