Albert Einstein allegedly called compound interest "the eighth wonder of the world." Whether or not he actually said it, the math behind compound interest is genuinely remarkable — and understanding it is essential for anyone making financial decisions about savings, investments, loans, or retirement planning.
Simple vs Compound Interest
Simple interest is calculated only on the original principal: Interest = P x r x t. If you invest $10,000 at 5% simple interest, you earn $500 every year regardless of how much has accumulated.
Compound interest is calculated on the principal plus all previously earned interest. Each period's interest earns interest in the next period, creating exponential growth.
| Year | Simple Interest (5%) | Compound Interest (5%) | Difference |
|---|---|---|---|
| 1 | $10,500 | $10,500 | $0 |
| 5 | $12,500 | $12,763 | $263 |
| 10 | $15,000 | $16,289 | $1,289 |
| 20 | $20,000 | $26,533 | $6,533 |
| 30 | $25,000 | $43,219 | $18,219 |
The Compound Interest Formula
A = P(1 + r/n)^(nt)
- A = Final amount (principal + interest)
- P = Principal (initial investment)
- r = Annual interest rate (as a decimal: 5% = 0.05)
- n = Number of times interest compounds per year
- t = Number of years
Compounding Frequency Matters
$10,000 at 5% for 10 years with different compounding frequencies:
| Frequency | n per year | Final Amount | Interest Earned |
|---|---|---|---|
| Annually | 1 | $16,288.95 | $6,288.95 |
| Quarterly | 4 | $16,386.16 | $6,386.16 |
| Monthly | 12 | $16,470.09 | $6,470.09 |
| Daily | 365 | $16,486.65 | $6,486.65 |
| Continuous | ∞ | $16,487.21 | $6,487.21 |
More frequent compounding helps, but the difference between daily and continuous compounding is negligible.
The Rule of 72
To estimate how long it takes to double your money, divide 72 by the annual interest rate: Years to double ≈ 72 / r.
- At 4%: ~18 years to double
- At 6%: ~12 years to double
- At 8%: ~9 years to double
- At 10%: ~7.2 years to double
- At 12%: ~6 years to double
The Power of Starting Early
$5,000 invested annually at 7% return:
| Starting Age | Total Contributed | Value at Age 65 | Interest Earned |
|---|---|---|---|
| 25 (40 years) | $200,000 | $1,068,048 | $868,048 |
| 35 (30 years) | $150,000 | $505,365 | $355,365 |
| 45 (20 years) | $100,000 | $219,326 | $119,326 |
Starting 10 years earlier with the same contribution more than doubles the final amount. Time is the most powerful variable in the compound interest formula.
Calculate compound interest scenarios with the WizlyTools Compound Interest Calculator.