The compound interest formula calculates how an investment grows when interest is added not just to the original principal, but to the accumulated interest as well. This is what separates compound growth from simple interest, and it's the mathematical foundation behind fixed deposits, savings accounts, and most long-term investment projections.
Formula
A = P ร (1 + r/n)โฟแต
| Variable | Meaning |
|---|---|
| A | Final amount (principal + interest) |
| P | Principal (initial investment) |
| r | Annual interest rate (as a decimal, e.g. 8% = 0.08) |
| n | Number of times interest compounds per year |
| t | Number of years |
To find just the interest earned: Compound Interest = A โ P
Worked Example
โน1,00,000 invested at 8% annual interest, compounded quarterly (n = 4), for 5 years:
- A = 1,00,000 ร (1 + 0.08/4)^(4ร5) = 1,00,000 ร (1.02)ยฒโฐ = โน1,48,595
- Compound Interest = โน1,48,595 โ โน1,00,000 = โน48,595
Compare that to simple interest on the same numbers: โน1,00,000 ร 0.08 ร 5 = โน40,000. The extra โน8,595 comes entirely from interest earning interest across the 20 compounding periods.
Key Things to Know
- Higher compounding frequency always produces a slightly higher final amount for the same nominal rate โ quarterly beats annual, monthly beats quarterly โ but the improvement shrinks as frequency increases; going from monthly to daily compounding barely moves the number.
- Time matters more than compounding frequency. Doubling the investment duration has a far larger effect on the final amount than switching from annual to monthly compounding at the same rate.
- Banks often quote a nominal rate but compound quarterly, which means the effective annual rate you actually earn is slightly higher than the quoted rate โ check the compounding frequency, not just the headline percentage, when comparing fixed deposits.
- This formula assumes no withdrawals or additional contributions. For a series of regular contributions (like a monthly SIP), the SIP Formula accounts for each instalment compounding separately instead.