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.
Analogy — Think of Simple Interest like a flat monthly rent that never changes, and Compound Interest like a snowball rolling downhill. SI pays interest only ever on the original amount (P) — the "rent" is always calculated on the same base. CI pays interest on the original amount PLUS all the interest already earned so far — each year's interest becomes part of next year's base, exactly like a snowball picking up more snow (and more surface area to pick up even more snow) as it rolls. That's precisely why CI grows faster than SI over time even at the identical rate — the base itself is growing, not staying flat.
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.
Revision Notes
Try It (2 Minutes)
Take ₹1000 at 10% per year for 3 years. Calculate SI and CI separately by hand, year by year for CI (don't use the formula shortcut yet): Year 1 both give ₹100 interest — identical. Year 2: SI still gives ₹100 (always on the original ₹1000), but CI gives 10% of ₹1100 (last year's total) = ₹110. Notice the gap only appears from Year 2 onward, not Year 1 — because CI only starts compounding once there's accumulated interest to compound on top of.