How Compound Interest Works
Compound interest is often called the "eighth wonder of the world." Unlike simple interest (calculated only on the principal), compound interest earns interest on your accumulated interest — creating exponential growth over time.
The Compound Interest Formula
A = P(1 + r/n)nt
- A = final amount
- P = initial principal
- r = annual interest rate (as decimal)
- n = number of times interest compounds per year
- t = number of years
With Monthly Contributions
When adding regular contributions, the formula extends to include the future value of an annuity:
A = P(1 + r/n)nt + PMT × [((1 + r/n)nt - 1) / (r/n)]
Where PMT = periodic contribution amount.
Example
$10,000 invested at 7% annually for 20 years with $200/month contributions:
- Initial investment: $10,000
- Total contributions: $48,000 ($200 × 240 months)
- Total interest earned: ~$66,000
- Final balance: ~$124,000
Your money more than doubled through compound interest alone.
The Rule of 72
A quick way to estimate how long it takes to double your money: divide 72 by the annual return rate.
- At 6%: 72/6 = 12 years to double
- At 8%: 72/8 = 9 years to double
- At 10%: 72/10 = 7.2 years to double
- At 12%: 72/12 = 6 years to double
Compounding Frequency
Interest can compound annually, semi-annually, quarterly, monthly, or daily. More frequent compounding produces slightly higher returns. On $10,000 at 5% for 10 years:
- Annually: $16,288.95
- Monthly: $16,470.09
- Daily: $16,486.65
The difference between monthly and daily compounding is small ($16.56 on $10K over 10 years), but between annual and monthly it's more noticeable ($181.14).