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 mean?
n is how many times interest is added per year (12 for monthly) and t is the number of years 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.
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 also earns on accumulated interest, so it grows faster.
The compound interest formula
Compound interest is calculated with A = P(1 + r/n)^(nt), giving 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, r the annual interest rate as a decimal, n how many times interest compounds per year, and t the number of years. The interest earned is 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. That £348.85 of interest beats the £300 simple interest would give.
More frequent compounding raises the total slightly — daily beats monthly, which beats annual. At the limit of continuous compounding the formula becomes A = Pe^(rt), using the constant e.
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