Compound Interest Formula
How interest earns interest — the formula, the variables, and two worked examples.
A = P (1 + r/n)nt
Compound interest earned: CI = A − P
Continuous compounding variant: A = P·ert (n → ∞)
What each variable means
| Symbol | Meaning | Example |
|---|---|---|
| P | Principal (starting amount) | ₹10,000 |
| r | Annual nominal rate as a decimal (not percent) | 8% → 0.08 |
| n | Times interest is credited per year | monthly → 12 |
| t | Time in years (fractions allowed) | 2.5 |
| A | Final amount (value of the investment) | result |
The rate conversion matters
With quarterly compounding at 8%, each quarter earns one quarter of the nominal rate: r/n = 0.08/4 = 0.02, and the exponent counts total periods: nt = 4 × 2 = 8 per two years. Mixing these up is the most common exam mistake.
Worked example 1 — annual
₹10,000 at 8% compounded annually for 2 years:
- A = 10,000 × (1 + 0.08/1)1×2 = 10,000 × 1.08²
- = 10,000 × 1.1664 = ₹11,664
- CI = 11,664 − 10,000 = ₹1,664
Worked example 2 — monthly
Same money, same rate, monthly compounding for 2 years:
- A = 10,000 × (1 + 0.08/12)12×2 = 10,000 × (1.006666…)24
- ≈ 10,000 × 1.17288 = ₹11,728.80
- CI ≈ ₹1,728.80 — ₹64.80 more than annual, purely from frequency.