Compound Interest

Interest computed on the principal and on previously accumulated interest, growing geometrically.

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Interest computed on the principal and on previously accumulated interest, growing geometrically.

Compound interest adds interest to the principal at the end of each compounding period so that the next period earns interest on the larger amount. With principal P, annual interest rate r, compounding n times per year, and time t in years, the final amount is A = P · (1 + r/n)^(n·t). For annual compounding (n = 1) this reduces to A = P · (1 + r)^t. Compound interest grows geometrically (multiplicatively), unlike simple interest which grows linearly.

A = P · (1 + r/n)^(n·t)

$1,000 at 5% annually for 3 years → A = 1000 · 1.05^3 ≈ $1,157.63
€500 at 4% compounded quarterly for 2 years → A = 500 · (1.01)^8 ≈ €541.43
$2,000 at 6% compounded monthly for 1 year → A = 2000 · (1.005)^12 ≈ $2,123.36

How to recognize it

Problem mentions 'compound', 'compounded monthly/yearly/daily', or 'annual yield'
Growth multiplies each period rather than adds
The balance accelerates over time (convex upward curve)

Common mistakes

Using simple interest when compounding is specified
Forgetting to divide the rate by the compounding frequency (r/n, not r)
Using n in place of n·t in the exponent

Practice guidance

Numerical Reasoning