Compound Interest Formula
Learn the compound interest formula using principal, annual rate, compounding frequency and time.
A = P(1 + r ÷ n)^(n × t)What the formula means.
Divide the annual rate by the number of compounding periods per year, add one, raise that factor to the total number of compounding periods, then multiply by principal.
More frequent compounding changes the effective annual growth.
The basic formula assumes a fixed rate and no additional contributions.
Interest earned equals future amount minus principal.
Variables.
ABalance after compounding.
PStarting amount.
rAnnual interest rate expressed as a decimal.
nHow many times interest is compounded each year.
tNumber of years.
Worked example.
- r ÷ n = 0.06 ÷ 12 = 0.005
- n × t = 12 × 10 = 120
- $10,000 × (1.005)^120 ≈ $18,193.97
Common mistakes.
- Entering 6 instead of 0.06 inside the formula.
- Mixing months and years without adjusting n and t.
- Using this basic formula when periodic contributions are part of the scenario.
Quick questions.
What is the difference between simple and compound interest?
Simple interest is calculated only on principal; compound interest also earns interest on accumulated interest.
Does monthly compounding mean the rate is 6% every month?
No. A 6% nominal annual rate compounded monthly uses 0.06 ÷ 12 per monthly period.