Albert Einstein allegedly called compound interest the “eighth wonder of the world.” Whether he said it or not, the math behind compound interest is genuinely powerful β and understanding it can transform how you save, invest, and borrow.
What Is Compound Interest?
Compound interest is interest calculated on both the initial principal and the accumulated interest from previous periods. Unlike simple interest (which only earns on the principal), compound interest causes your money to grow exponentially.
Compound Interest: $1,000 at 10% compounded annually for 3 years = $1,331 ($331 earned)
The Compound Interest Formula
- A = Final amount (principal + interest)
- P = Principal (starting amount)
- r = Annual interest rate (as a decimal: 5% = 0.05)
- n = Number of times interest compounds per year
- t = Time in years
Step-by-Step Example
You invest $5,000 at 6% annual interest, compounded monthly, for 10 years.
- P = $5,000 | r = 0.06 | n = 12 | t = 10
- r/n = 0.06 Γ· 12 = 0.005
- n Γ t = 12 Γ 10 = 120
- 1 + 0.005 = 1.005
- 1.005^120 = 1.8194
- A = 5,000 Γ 1.8194 = $9,097
Result: Your $5,000 grows to $9,097. Interest earned = $4,097 β more than doubling your investment!
How Compounding Frequency Affects Growth
Same $5,000 at 6% for 10 years β different compounding frequencies:
| Compounding | n | Final Amount | Interest Earned |
|---|---|---|---|
| Annually | 1 | $8,954 | $3,954 |
| Quarterly | 4 | $9,070 | $4,070 |
| Monthly | 12 | $9,097 | $4,097 |
| Daily | 365 | $9,110 | $4,110 |
More frequent compounding = slightly higher returns, but the difference narrows as frequency increases.
The Rule of 72 β Quick Doubling Estimate
Want to know how long it takes to double your money? Divide 72 by your annual interest rate:
At 6%: 72 Γ· 6 = 12 years to double
At 8%: 72 Γ· 8 = 9 years to double
At 12%: 72 Γ· 12 = 6 years to double
Compound Interest on Debt (The Other Side)
Compound interest works against you on debt. A credit card with 22% APR compounded monthly:
- $5,000 balance with minimum payments β can take 15+ years to pay off
- Total interest paid can exceed the original balance
This is why paying off high-interest debt is often better than investing at a lower return rate.