How the compound interest formula works
With compound interest, each period's interest is added to the balance, so later interest is earned on interest as well. The calculator uses the standard closed form:
A = P × (1 + r / n)n × t
Pis the principal, the amount you start with.ris the annual rate as a decimal (8% is 0.08).nis the number of compounding periods per year. The dropdown offers annually (1), semi-annually (2), quarterly (4), monthly (12) and daily (365).tis the time in years.
The Final amount is A and the Interest earned is A − P. This is a lump-sum calculation: there are no regular deposits or withdrawals, and no tax or fees.
Worked example and the effect of frequency
Take 10,000 at 8% for 10 years. Compounded annually, A = 10,000 × 1.0810 = 21,589. Compounded monthly, A = 10,000 × (1 + 0.08/12)120 = 22,196. The extra 607 comes purely from interest being credited more often.
| Compounding (10,000, 8%, 10 yrs) | Final amount | Interest earned |
|---|---|---|
| Annually | 21,589 | 11,589 |
| Semi-annually | 21,911 | 11,911 |
| Quarterly | 22,080 | 12,080 |
| Monthly | 22,196 | 12,196 |
| Daily | 22,253 | 12,253 |
The gains shrink as frequency rises. Moving from annual to monthly adds about 607, but from monthly to daily only about 57. Even continuous compounding (P × ert) would give just 22,255. Time and rate matter far more: at 8% monthly, the same 10,000 becomes 49,268 after 20 years and 1,09,357 after 30. At a lower 6% for 10 years it reaches 18,194.
Rules of thumb and pitfalls
- Rule of 72. Divide 72 by the annual rate to estimate the doubling time. At 8% that is 9 years, and the exact figure is about 9.006.
- Nominal versus effective rate. 8% compounded monthly is an effective annual yield of about 8.30%. When comparing a savings account to a bond, compare effective annual yields (APY), not the headline nominal rates.
- Debt compounds too. The same formula describes a credit-card balance that is left unpaid, which is why a high rate with frequent compounding grows quickly.
- Real returns. Inflation and tax erode the figure. The inflation calculator helps adjust for it.
If you add money every month, use the SIP calculator, which models recurring deposits. For interest that does not compound, see the simple interest calculator, and read compound interest explained for the intuition behind the curve.