How compound interest works
Compound interest is the interest calculated on the initial principal and also on the accumulated interest from previous periods. Think of it as interest on interest — it makes your money grow at an accelerating rate rather than a linear one.
The core formula is:
A = P(1 + r/n)nt
- P = initial principal (starting amount)
- r = annual interest rate (as a decimal, e.g. 0.05 for 5%)
- n = number of times interest is compounded per year
- t = number of years
If you add recurring contributions, their future value is added separately using the future value of an annuity formula.
Example scenario
Starting with $10,000 at an annual rate of 5% (compounded monthly) and adding $200/month for 10 years:
- Total contributions: $34,000
- Total interest earned: ~$13,500
- Future value: ~$47,500
Why the compounding frequency matters
The more frequently interest is compounded, the higher your total return. Daily compounding slightly beats monthly, which beats annual. Most savings accounts and investment returns compound monthly or daily, so selecting the matching frequency gives the most accurate estimate.