Math & Everyday Life
Simple vs Compound Interest: What's the Difference?
Understand the difference between simple and compound interest — the formulas, worked examples, and why compounding makes such a large difference over time.
Interest is the cost of borrowing money — or the reward for saving it. Whether you're taking out a loan, putting money in a savings account, or investing, understanding how interest compounds (or doesn't) has an enormous effect on the final amount.
Simple Interest
Simple interest is calculated only on the original principal. Formula: Interest = P × r × t. Where P = principal, r = annual interest rate (as a decimal), t = time in years. $1,000 at 5% for 3 years: 1,000 × 0.05 × 3 = $150 interest. Total: $1,150.
Compound Interest
Compound interest is calculated on both the principal and the accumulated interest. Formula: A = P × (1 + r/n)^(nt). Where n = compounding periods per year. $1,000 at 5% compounded annually for 3 years: 1,000 × (1.05)³ = $1,157.63. An extra $7.63 compared to simple interest — seemingly small, but the gap widens dramatically over time.
The Power of Time
- $10,000 at 7% simple interest for 30 years: $31,000
- $10,000 at 7% compound interest (annual) for 30 years: $76,122
- $10,000 at 7% compound interest (monthly) for 30 years: $81,165
The Rule of 72
Quick shortcut: divide 72 by the annual interest rate to estimate how many years it takes for your money to double. At 6% interest: 72 ÷ 6 = 12 years to double. At 8%: 72 ÷ 8 = 9 years. At 3%: 72 ÷ 3 = 24 years.
Compound interest works against you in debt. A credit card charging 20% APR doubles your balance in about 3.6 years if you make no payments — that's 72 ÷ 20.