Compound interest is interest calculated on both the original principal and the interest already accumulated. Unlike simple interest, which calculates only on the original amount, compound interest grows exponentially — which is why Albert Einstein reportedly called it "the eighth wonder of the world." The difference between simple and compound interest becomes dramatic over long time horizons.
Simple vs Compound Interest — Example
Principal: $10,000. Annual rate: 7%. Time: 20 years.
- Simple interest: $10,000 × 7% × 20 = $14,000 interest earned. Total = $24,000.
- Compound interest (annual): $10,000 × (1.07)²⁰ = $38,697. Interest earned = $28,697.
- Compound interest (monthly): $10,000 × (1 + 0.07/12)²⁴⁰ = $40,064. Interest earned = $30,064.
Monthly compounding adds over $1,300 vs annual compounding over 20 years — purely from the frequency of reinvestment.
Compounding Frequency Comparison Table
| Frequency | Times per Year | $10,000 @ 6% after 10 years |
|---|---|---|
| Annual | 1 | $17,908 |
| Quarterly | 4 | $18,061 |
| Monthly | 12 | $18,194 |
| Daily | 365 | $18,220 |
The Rule of 72
A quick mental shortcut: divide 72 by the annual interest rate to estimate how many years it takes to double your money. At 6% per year: 72 ÷ 6 = 12 years to double. At 9%: 72 ÷ 9 = 8 years. At 3%: 72 ÷ 3 = 24 years. This rule is accurate within a few percent for rates between 2% and 20% and is widely used in financial planning as a first-pass estimate.
Compound Interest in Debt
Compound interest works against you in debt. Credit card balances at 20–29% APR compound monthly. A $5,000 credit card balance at 24% APR, with only minimum payments made, can take over 15 years to pay off and cost more than $7,000 in interest — more than the original balance. The same mathematics that builds wealth in savings destroys it in high-interest debt. Paying off high-interest debt is mathematically equivalent to earning that interest rate risk-free.