Compound Interest

The Story

Meera put ₹10,000 into a fixed deposit earning 10% per year, compounded annually, for 2 years. Arjun, thinking of simple interest, computed SI = (10000×10×2)/100 = ₹2,000, expecting a final amount of ₹12,000. But Meera's actual statement showed ₹12,100 — ₹100 more.

"Compound interest works differently," Meera explained. "Each year, interest is calculated on the AMOUNT so far — principal PLUS all interest already earned — not just on the original principal." Year 1: interest = 10% of 10,000 = 1,000, so amount becomes 11,000. Year 2: interest = 10% of 11,000 (not 10,000!) = 1,100, so amount becomes 12,100.

"That extra ₹100 in year 2," she said, "is interest earned ON the ₹1,000 interest from year 1. That's what 'compounding' means — interest earns its own interest." Arjun compared: under simple interest, year 2 would have earned exactly the same ₹1,000 as year 1, since SI always uses the original principal.

Meera then showed the direct formula, instead of computing year by year: Amount = P(1 + R/100)ⁿ, where P is principal, R is the annual rate, and n is the number of years. For her deposit: A = 10000×(1.10)² = 10000×1.21 = 12,100 — matching the year-by-year calculation exactly. Compound Interest (CI) = Amount − Principal = 12,100 − 10,000 = 2,100.

Arjun tried the formula on a 3-year, 5% deposit of ₹8,000: A = 8000×(1.05)³ = 8000×1.157625 = 9,261. CI = 9,261 − 8,000 = 1,261. He compared to SI on the same numbers: (8000×5×3)/100 = 1,200. "CI is always bigger than SI over the same period, whenever the rate is positive," he noticed, "and the gap grows with more years."

By the end, both had the key distinction clear: simple interest is always calculated on the ORIGINAL principal (same amount every year); compound interest is calculated on the GROWING amount (principal plus all interest so far), which is why it always outpaces simple interest over time.