The Compound Interest Formula (With Examples)
The compound interest formula A = P(1 + r/n)^(nt) explained term by term, with a worked example and the continuous‑compounding version.
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Frequently asked questions
What is the compound interest formula?
A = P(1 + r⁄n)^(nt), where A is the final amount, P the principal, r the annual rate, n the compounds per year and t the years.
What do n and t represent?
n is how many times interest is added per year (12 for monthly), and t is the number of years the money is invested.
How do I find just the interest earned?
Subtract the principal from the final amount: interest = A − P.
Does more frequent compounding earn more?
Yes, slightly. Daily compounding beats monthly, which beats annual, for the same rate — though the differences are small.
What is continuous compounding?
The limit of ever-more-frequent compounding, given by A = Pe^(rt), where e is about 2.718.
How is this different from simple interest?
Simple interest (I = Prt) is earned only on the principal; compound interest is also earned on accumulated interest, so it grows faster.
The compound interest formula
Compound interest is calculated with A = P(1 + r⁄n)^(nt), which gives the final amount A from a starting principal that earns interest on both the original sum and the interest already added.
What each symbol means
P is the principal (starting amount), r is the annual interest rate as a decimal, n is how many times interest compounds per year, and t is the number of years. The interest earned is simply A − P.
Worked example
$1,000 at 6% compounded monthly for 5 years: n=12, r=0.06, t=5, so A = 1000 × (1 + 0.06⁄12)^(12×5) = 1000 × (1.005)^60 ≈ $1,348.85. The $348.85 of interest is more than the $300 simple interest would give, because of compounding.
More frequent compounding raises the total slightly: the same deposit compounded daily beats monthly, which beats annually. At the limit of continuous compounding the formula becomes A = Pe^(rt), using the constant e.
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