gen-define-compound-interest-and-give-one-short-worked-example-0666

Define compound interest and give one short worked example.

# Compound Interest **Compound interest** is interest calculated on both the initial principal AND the accumulated interest from previous periods. In other words, it's "interest on interest," which makes your money grow faster than simple interest. ## Formula **A = P(1 + r)^t** Where: - A = final amount - P = principal (initial amount) - r = interest rate per period (as a decimal) - t = number of time periods ## Worked Example **Problem:** You invest $1,000 at 5% annual interest, compounded yearly. How much will you have after 3 years? **Solution:** - P = $1,000 - r = 0.05 - t = 3 A = 1,000(1 + 0.05)³ A = 1,000(1.05)³ A = 1,000(1.157625) **A = $1,157.63** You earn **$157.63** in interest, compared to only $150 with simple interest (where you'd earn $50 per year). The extra $7.63 comes from earning interest on your interest.