Compound Interest Formula: The Complete Guide With Examples

The compound interest formula

A = P × (1 + r/n)^(n × t)

• A — Final amount (principal + interest)
• P — Principal (the money you start with)
• r — Annual interest rate (as decimal — 8% = 0.08)
• n — Number of times interest is compounded per year
• t — Time in years

Compound interest earned = A − P

The simple interest formula (for comparison)

SI = (P × r × t) / 100

Simple interest earns on the original principal only. Compound interest earns on the principal plus previously accumulated interest — that's where the exponential magic comes from.

Example 1: Annual compounding

Invest ₹10,000 at 10% per year for 3 years, compounded yearly.

• n = 1, r = 0.10, t = 3
• A = 10,000 × (1 + 0.10)^3 = 10,000 × 1.331 = ₹13,310
• Interest earned = ₹3,310

Example 2: Monthly compounding

Same ₹10,000 at 10%, compounded monthly for 3 years.

• n = 12, r = 0.10, t = 3
• A = 10,000 × (1 + 0.10/12)^(12 × 3) = 10,000 × (1.00833)^36 ≈ ₹13,482

Monthly compounding earns ₹172 more than yearly — small, but real.

Example 3: Quarterly compounding

Same ₹10,000 at 10%, compounded quarterly for 3 years.

• n = 4, r = 0.10, t = 3
• A = 10,000 × (1 + 0.10/4)^(4 × 3) = 10,000 × (1.025)^12 ≈ ₹13,449

Compound interest vs simple interest

Over 20 years at 12%, ₹1 lakh becomes: - Simple interest: ₹3.4 lakh - Compound interest: ₹9.6 lakh

Same money. Same rate. Compounding just kept multiplying.

Common bank exam trap

If a question says "compounded half-yearly", n = 2 and you use half the annual rate for each period. Read the question twice.

The rule of 72

Want to know how many years to double your money? Divide 72 by the interest rate.

• 6% → 12 years
• 9% → 8 years
• 12% → 6 years

Approximate, but scarily accurate for bank exam MCQs.

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