Simple & Compound Interest – Patwari / Lekhpal Study Notes
(Quantitative Aptitude – Jammu & Kashmir Patwari / Lekhpal Programme)
1. Simple Explanation
| Concept | What it means | How it works |
|---|---|---|
| Simple Interest (SI) | Interest earned only on the original principal for the whole period. | SI = (P × r × t) / 100 |
| Compound Interest (CI) | Interest earned on the principal and on the interest that has accumulated in previous periods. | A = P (1 + r/n)^(n t) CI = A – P |
- P – Principal amount (initial sum of money)
- r – Annual rate of interest (in % per annum)
- t – Time period (in years)
- n – Number of times interest is compounded per year
- A – Maturity value (amount after t years)
Key Idea:
Simple → Only the original sum earns interest.
Compound → The sum grows each period because interest is added to the principal, so the next period earns interest on a larger base.
2. Key Points to Remember
| Topic | Take‑away |
|---|---|
| SI Formula | SI = (P × r × t) / 100 |
| CI Formula | A = P (1 + r/n)^(n t) CI = A – P |
| Effective Annual Rate (EAR) | EAR = (1 + r/n)^n – 1 |
| When n = 1 | Compounding once a year → A = P (1 + r/100)^t |
| When n = 12 | Monthly compounding → A = P (1 + r/(12×100))^(12 t) |
| Interest on Interest | In CI, each period’s interest is added to the principal, so next period’s interest includes the previous interest. |
| Time, Rate, or Principal Problems | Use logarithms or algebraic manipulation: • r = (A/P)^(1/(nt)) – 1 (convert to percent: ×100) • t = ln(A/P) / [n ln(1 + r/n)] |
| Rule of 72 | Approximate years to double at rate r%: Years ≈ 72 / r |
| Rule of 115 | Approximate years to reach 100% interest at rate r%: Years ≈ 115 / r |
| Typical Exam Tricks | • Convert rates to decimal before calculations. • For small rates or short periods, A ≈ P (1 + r t/100) works well. • Use logarithms only when calculator permits. |
3. Worked Example
Problem
A patwari deposits ₹12,000 in a bank at an annual interest rate of 6% compounded quarterly for 4 years.
Find:
- The maturity value (A).
- The total compound interest earned.
Solution
| Step | Calculation | Result |
|---|---|---|
| 1. Identify variables | P = ₹12,000, r = 6% = 0.06, n = 4, t = 4 | — |
2. Compute 1 + r/n |
1 + 0.06/4 = 1 + 0.015 = 1.015 |
— |
3. Compute exponent n t |
4 × 4 = 16 |
— |
4. Compute (1 + r/n)^(n t) |
1.015^16 (calculator) ≈ 1.26824 |
— |
| 5. Multiply by P | A = 12,000 × 1.26824 ≈ ₹15,218.88 |
— |
| 6. Compound Interest | `CI = A – P = 15,218. |