Simple and Compound Interest
Why This Chapter Matters
SI and CI gives 3-5 questions in SSC CGL and CHSL. Also appears in banking exams. Once you know the formulas and shortcuts, these are fast marks.
Core Concepts
Simple Interest (SI)
SI = PRT/100 | Amount A = P + SI = P(1 + RT/100)
P = Principal | R = Rate % per annum | T = Time (years)
Compound Interest (CI)
Amount A = P(1 + R/100)ⁿ | CI = A - P
n = number of compounding periods.
Compounding frequency:
Half-yearly: A = P(1 + R/200)^(2n)
Quarterly: A = P(1 + R/400)^(4n)
Monthly: A = P(1 + R/1200)^(12n)
CI-SI Difference Shortcuts
For 2 years: CI - SI = P(R/100)²
For 3 years: CI - SI = P(R/100)²(3 + R/100)
Effective Rate
If CI rate=R% compounded half-yearly, effective annual rate = (1+R/200)²-1 × 100%.
Common Shortcuts
Rule of 72: Years to double money = 72/R (approximate).
At 8%: doubles in 72/8=9 years. At 12%: 72/12=6 years.
Finding rate given CI and time:
If amount becomes A in n years, R% = [(A/P)^(1/n) - 1] × 100.
Solved Examples
Q1: Find SI on Rs 8000 at 15% for 3 years.
SI = 8000×15×3/100 = Rs 3600. Amount = Rs 11600.
Q2: Rs 5000 at 10% CI for 2 years. CI and difference from SI?
A = 5000(1.1)² = 5000×1.21 = Rs 6050. CI = Rs 1050.
SI = 5000×10×2/100 = Rs 1000. Difference = Rs 50.
Check: P(R/100)² = 5000×(0.1)² = 5000×0.01 = 50 ✓
Q3: A sum doubles in 10 years at SI. In how many years does it triple?
SI makes money = 2P in 10 years → SI per year = P/10.
To triple: SI needed = 2P → time = 2P/(P/10) = 20 years.
PYQs (SSC)
SSC CGL 2023: At what rate% CI does Rs 2000 become Rs 2420 in 2 years?
2420 = 2000(1+R/100)² → (1+R/100)² = 1.21 → 1+R/100=1.1 → R=10%.
SSC CHSL 2022: Difference between CI and SI on Rs 10000 for 2 years at 5%?
CI-SI = P(R/100)² = 10000×(0.05)² = 10000×0.0025 = Rs 25.