Simple Interest vs Compound Interest: CA Foundation Maths
The choice between simple and compound interest can mean the difference of thousands of rupees over time. This is a fundamental concept in CA Foundation Business Mathematics.
head-to-Head Comparison
| Basis | Simple Interest (SI) | Compound Interest (CI) |
|---|---|---|
| Basis of Calculation | Interest calculated on the Original Principal only | Interest calculated on Principal + Accumulated Interest (compounding) |
| Formula | SI = (P × R × T) / 100 | CI: A = P(1 + r/n)^(nt); CI = A − P |
| Growth Pattern | Linear growth — interest amount is the same every period | Exponential growth — interest amount increases every period |
| Amount After n Years | A = P(1 + RT/100) — grows linearly | A = P(1 + r)^n — grows exponentially |
| Practical Usage | Short-term loans, simple savings, flat rate car loans | Fixed deposits, mutual funds, long-term investments, EMI calculations |
The 'CI > SI by a Specific Formula' Trap
For 2 years, CI − SI = P(r/100)². This formula allows you to find P, r, or the difference directly without full computation. For 3 years: CI − SI = P(r/100)²(r/100 + 3). Memorize these shortcuts for exam speed.
Common Ground (Similarities)
- Both compute interest on a principal amount at a given rate for a given period.
- When interest is compounded annually for 1 year, SI and CI give the same result.
- Both are essential for valuing annuities, loans, and investments in financial mathematics.
Test Your Understanding
Q1: SI on ₹10,000 at 10% for 3 years is:
₹3,100
₹3,310
₹3,000 ✅
₹2,700
Explanation: SI = (10,000 × 10 × 3) / 100 = ₹3,000. Simple interest is always the same each year.
Q2: The difference between CI and SI for 2 years at 10% on ₹10,000 is:
₹0
₹10
₹100 ✅
₹1,000
Explanation: CI − SI for 2 years = P(r/100)² = 10,000 × (0.1)² = 10,000 × 0.01 = ₹100.