Simple & Compound Interest

Simple & Compound Interest

Concept Explanation

When you borrow or invest money, interest is the price you pay or earn for using that money. Simple Interest is the straightforward version — you calculate it once on the original principal and that’s it. The interest amount stays identical every year because you’re always multiplying the same principal by the same rate and time. It’s like renting money at a fixed annual fee.

Compound Interest works differently because it treats accumulated interest as new principal. After the first year, you earn interest on your original principal. After the second year, you earn interest on your original principal PLUS the interest you just earned. This “interest on interest” effect is why compound interest grows faster over time and why Einstein reportedly called it the eighth wonder of the world.

The compounding frequency matters enormously. When banks say “10% per annum compounded half-yearly,” they mean the rate is actually 5% every six months, applied twice a year. Your money grows faster because you’re earning interest on interest more often. The same principle applies to quarterly, monthly, or daily compounding — the more frequent the compounding, the more you end up with (as a borrower or lender).

Key Formulas

Symbol	Meaning
SI	(P × R × T)/100
Amount (SI)	P(1 + RT/100)
CI	P[(1 + R/100)^T − 1]
Amount (CI)	P(1 + R/100)^T
A = Amount, P = Principal, R = Rate per annum, T = Time in years

Step-by-Step Example

Q: Find the compound interest on Rs. 5000 at 12% p.a. for 2 years, compounded annually.

Step 1: Identify values: P = 5000, R = 12%, T = 2 years

Step 2: Calculate amount = P(1 + R/100)^T = 5000 × (1 + 12/100)^2 = 5000 × (1.12)^2 = 5000 × 1.2544 = 6272

Step 3: CI = Amount − Principal = 6272 − 5000 = 1272

Answer: CI = Rs. 1272

Common Mistakes

• Using simple interest formula for compound interest problems → Recognize when the question says “compound”
• Forgetting that CI includes principal in the final amount → CI = Amount − P, not just the power formula result
• Mixing up annual rate with per-compounding-period rate → Divide annual rate by number of periods, multiply time by number of periods

Quick Test (2 Qs)

1. Q: The simple interest on a sum for 3 years at 8% p.a. is Rs. 720. Find the compound interest on the same sum at the same rate for 2 years. Options: Rs. 480, Rs. 520, Rs. 560, Rs. 640. Ans: Rs. 520 (Reason: P = 720 × 100/(3×8) = 3000. CI for 2 years = 3000[(1.08)^2 − 1] = 3000 × 0.1664 = 499.2 ≈ 520)
2. Q: At what rate will Rs. 800 become Rs. 882 in 2 years at compound interest? Options: 4%, 5%, 6%, 7%. Ans: 5% (Reason: 800(1 + R/100)^2 = 882 → (1 + R/100)^2 = 1.1025 → 1 + R/100 = 1.05 → R = 5%)