SI CI Master - Quick Revision
SI CI Master - Quick Revision
One-Liners
- SI = P×R×T / 100 – interest stays same every year.
- CI = P(1 + r/100)^t – P – interest earns interest.
- If rate is half-yearly, divide R by 2 & multiply T by 2.
- If quarterly, divide R by 4 & multiply T by 4.
- Effective annual rate = (1 + r/n)^n – 1.
- CI for 2 yrs ≈ 2r + r²/100 (mental shortcut).
- Difference CI-SI for 2 yrs = P(r/100)².
- SI doubles in 100/r yrs; CI ≈ 72/r yrs (Rule-72).
- Instalment SI: each instalment = A / (1 + RT/100).
- Instalment CI: each instalment = A / (1 + r/100)^T.
- For 3 yrs, CI/SI ratio ≈ (3r² + r³/100) / 300.
- When T = 2, CI = SI + SI×r/200.
- Growth → CI; fixed return → SI.
- Population problems: treat population as P & rate as r.
- If sum becomes n times in t yrs SI, R = 100(n–1)/t.
- If sum becomes n times in t yrs CI, r = 100(n^(1/t) – 1).
- Successive % changes: effective = a + b + ab/100.
- Depreciation is just negative CI.
- Always convert time to years first.
- Rate must be % p.a. unless stated.
Formulas/Rules
| Formula | Use |
|---|---|
| SI = PRT/100 | Simple interest straight calc |
| A = P + SI = P(1 + RT/100) | Amount under SI |
| CI = P[(1 + r/100)^t – 1] | Compound interest |
| A = P(1 + r/100)^t | Amount under CI |
| Difference (2 yr) = P(r/100)² | CI – SI shortcut |
| Instalment (SI) = A / (1 + RT/100) | Equal instalment SI loan |
| Instalment (CI) = A / (1 + r/100)^T | Equal instalment CI loan |
| Effective rate = (1 + r/n)^n – 1 | Compare compounding frequencies |
| Rule-72: t ≈ 72/r | Doubling time (CI) |
| Sum from rate (SI): P = 100×SI / RT | Find principal |
Memory Tricks
- SI → “Same Interest” – every year same money.
- CI → “Compounding Ice-cream” – layers on layers.
- CI-SI difference 2 yrs → “Pee on Square Rate” = P (r%)².
- Rate half-yearly → “Half-rate, Double-time” (HRDT).
- Rule-72 → “7-2 twins” → 72 ÷ rate = doubling twins.
Common Errors
| Error | Correct |
|---|---|
| Using CI formula for half-yearly without halving rate | Divide yearly rate by 2, multiply time by 2 |
| Taking 3 months as 0.3 yr | 3 months = 0.25 yr |
| Forgetting to subtract P to get CI | CI = Amount – P |
| Adding CI & SI differences for 3 yrs like 2 yrs | Use P(r/100)²(3 + r/100) for 3-yr diff |
| Using SI instalment formula for CI loan | Use CI instalment formula with power term |
5 Quick MCQs
Show Questions
Q1. A sum doubles in 4 yrs at SI. Rate % is
A) 20% B) 25% C) 15% D) 12.5%
Ans: B) 25%
Q2. CI on ₹ 2000 for 2 yrs @ 10% p.a. is
A) ₹ 400 B) ₹ 420 C) ₹ 410 D) ₹ 441
Ans: B) ₹ 420
Q3. Difference b/w CI & SI on ₹ 5000 for 2 yrs is ₹ 50. Rate is
A) 8% B) 10% C) 12% D) 14%
Ans: B) 10%
Q4. Effective annual rate of 8% compounded quarterly is nearest to
A) 8.24% B) 8.30% C) 8.40% D) 8.50%
Ans: A) 8.24%
Q5. If CI for 3 yrs is ₹ 662 and for 2 yrs is ₹ 420, then rate is
A) 8% B) 10% C) 12% D) 15%
Ans: B) 10%
BETA
