Simple & Compound Interest

Simple & Compound Interest

Concept

Interest is basically the “rent” you pay for using someone else’s money, or the “bonus” you earn for lending yours. Simple Interest (SI) is the straightforward version: you borrow ₹10,000 at 8% per year, you pay 8% of ₹10,000 = ₹800 every single year, flat. The interest never changes because it’s always calculated on the original ₹10,000, never on the accumulated amount. So over 3 years, SI = ₹800 × 3 = ₹2,400.

Compound Interest (CI) is where it gets interesting. Instead of calculating interest on just the original principal, you calculate it on the accumulated amount each period. In year one, interest is 8% of ₹10,000 = ₹800, so you now owe ₹10,800. In year two, interest is 8% of ₹10,800 = ₹864. You’re now paying interest on interest — which is both good when you’re earning and painful when you’re borrowing.

The formula for CI is Amount = P(1 + R/100)^T. That exponent T is doing heavy lifting — it means you’re multiplying (1 + R/100) by itself T times. For 3 years at 8%, that’s (1.08)^3 = 1.2597, so ₹10,000 becomes ₹12,597. The extra ₹197 compared to SI (₹12,400) is the “interest on interest” effect.

When interest is compounded half-yearly (twice a year), the rate per half-year becomes R/2 and the number of periods becomes 2T. So 8% per annum compounded half-yearly means 4% every 6 months for 2 years (4 periods).

Key Formulas

Formula	Use
SI = (P × R × T) ÷ 100	Simple interest for one year
Amount (SI) = P + SI = P(1 + RT/100)	Total amount with SI
CI: A = P(1 + R/100)^T	Amount with CI (annual compounding)
CI − SI difference	Extra amount earned with CI vs. SI
Rate per period = R ÷ n, Periods = n × T	For n-times-per-year compounding

Worked Example

Q: Find the compound interest on ₹20,000 at 10% per annum for 2 years, compounded annually.

Step 1: Year 1 interest = 10% of 20,000 = ₹2,000 Year 1 amount = 20,000 + 2,000 = ₹22,000

Step 2: Year 2 interest = 10% of 22,000 = ₹2,200 Year 2 amount = 22,000 + 2,200 = ₹24,200

Step 3: CI = Final Amount − Principal = 24,200 − 20,000 = ₹4,200

Or use formula: A = 20000 × (1 + 10/100)^2 = 20000 × 1.1 × 1.1 = ₹24,200 → CI = 24,200 − 20,000 = ₹4,200

Answer: ₹4,200

Common Errors

• Using time T directly for half-yearly compounding → Convert properly: 2 years half-yearly means 4 periods at (R/2)% each
• Confusing SI and CI formulas → SI uses P × R × T (linear); CI uses P raised to power T (exponential)
• Forgetting to subtract the principal from CI → CI is not the final amount; it’s the interest portion only: CI = A − P