College Algebra / Unit 8 Alg 418 worked example, 60 to 90 seconds
Compound Interest
The idea
The compound interest formula grows a principal P at annual rate r compounded n times per year for t years: A = P(1 + r/n)^(nt).
In practice
Grow 1000 at 6% compounded monthly for 10 years. Read the parts: P = 1000, r = 0.06, n = 12, t = 10. The per-period rate is 0.06/12 = 0.005, and the period count is 12 · 10 = 120. So A = 1000(1.005)¹²⁰ ≈ 1819.40. The formula is an exponential function wearing a suit: the base 1.005 is the constant ratio, applied 120 times, and the reasonableness audit holds — the money nearly doubles in a decade at 6%, more than the 1600 that non-compounding interest would give, because interest here earns interest.
Where people slip
Convert the percent to a decimal and the years to periods before anything else.
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