Principal + rate + time → Final balance, total interest & year-by-year growth
| Frequency | Times/year | Effect |
|---|---|---|
| Annually | 1 | Baseline; simplest |
| Semi-annually | 2 | Slightly more than annual |
| Quarterly | 4 | Common for CDs and bonds |
| Monthly | 12 | Most savings accounts & mortgages |
| Daily | 365 | Approaches continuous compounding |
More frequent compounding always yields more interest — but the difference between monthly and daily is minimal for most practical purposes.
Compound interest means you earn interest on both your principal and the interest already earned. Unlike simple interest (calculated only on principal), compound interest accelerates growth exponentially — often called "the eighth wonder of the world."
A = P × (1 + r/n)^(n×t), where P = principal, r = annual rate (decimal), n = compounds per year, t = years. With monthly contributions: A = P(1+em)^(12t) + PMT × ((1+em)^(12t) − 1) / em, where em is the effective monthly rate.
Divide 72 by your annual interest rate to estimate how many years it takes to double your money. At 6% annual return: 72 ÷ 6 = 12 years to double. At 9%: 72 ÷ 9 = 8 years. This is a quick mental shortcut — the calculator above gives exact figures.
Enormously. $10,000 at 7% for 40 years grows to ~$149,745. The same amount for 30 years yields ~$76,123. The extra 10 years nearly doubles the result. Starting early is the single most powerful lever in long-term investing.