How to Calculate Compound Interest
What is Compound Interest?
Compound interest calculates interest on both the initial principal and the previously accumulated interest. Unlike simple interest (which only grows on the principal), compound interest grows exponentially — your interest earns interest. Einstein reportedly called it "the eighth wonder of the world."
Step-by-Step Guide
- 1Start with your principal amount P
- 2Determine the annual rate r and how often it compounds (n times per year)
- 3Apply the formula: A = P(1 + r/n)^(nt)
- 4The difference A − P is the total interest earned
Worked Examples
Input
$1,000 at 5% for 10 years (annual)
Result
$1,628.89
1000(1.05)¹⁰ — earned $628.89 interest
Input
$1,000 at 5% for 10 years (monthly)
Result
$1,647.01
Monthly compounding earns $18.12 more
Input
$5,000 at 7% for 20 years (annual)
Result
$19,348.42
Nearly 4× the initial investment
Input
$100/month for 30 years at 8%
Result
$149,035.94
Total invested: $36,000. Interest: $113,035
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