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 P is the principal, r the annual rate as a decimal, n the compounding periods per year, and t the number of years.
How do I calculate compound interest by hand?
Convert the rate to a decimal, divide by the number of periods per year, add 1, raise it to the power of periods × years, then multiply by the principal.
What is the formula for continuous compounding?
A = Pe^(rt), where e is about 2.71828. It gives the limit of the balance as compounding frequency increases without bound.
How do I find just the interest earned?
Calculate the final amount A, then subtract the principal P. The difference is the compound interest earned.
The Compound Interest Formula (With Examples)
The standard compound interest formula is:
A = P (1 + r/n)nt
What each term means
- A — the final amount (principal plus interest).
- P — the principal, your starting amount.
- r — the annual interest rate as a decimal (5% = 0.05).
- n — how many times interest compounds per year.
- t — the number of years.
Worked example
P = 1,000, r = 0.05, n = 12 (monthly), t = 10 years: A = 1,000 × (1 + 0.05/12)120 ≈ 1,647.01. The interest earned is about 647.01.
Continuous compounding
If interest compounds continuously, the formula becomes A = P ert, where e ≈ 2.71828. With the same numbers, A = 1,000 × e0.5 ≈ 1,648.72 — the practical ceiling as compounding gets more frequent.
Examples are illustrative and for general education, not financial advice.
Results are estimates for general guidance in India and may not reflect the latest local rates, fees or rules. Check official sources before making decisions.