Simple & Compound Interest
Program: Arunachal Pradesh Patwari / Lekhpal
Subject: Quantitative Aptitude
1. Simple Explanation
| Concept | What It Means | When It Applies |
|---|---|---|
| Principal (P) | Initial amount of money borrowed or invested. | All interest problems. |
| Rate (r) | Annual interest rate expressed as a percentage. | All interest problems. |
| Time (t) | Number of years (or fraction of a year) the money is borrowed/invested. | All interest problems. |
| Simple Interest (SI) | Interest calculated only on the principal, not on previously earned interest. | Loans where interest is paid at the end of the period. |
| Compound Interest (CI) | Interest earned on both the principal and accumulated interest. | Savings accounts, fixed deposits, loans with periodic compounding. |
Why it matters
- Simple interest is easier to compute and often used for short‑term loans.
- Compound interest grows faster; it’s the default for most savings instruments.
2. Key Points
| Point | Detail |
|---|---|
| Formula – Simple Interest | SI = (P × r × t) / 100 |
| Formula – Compound Interest | CI = P × (1 + r/100)^t – P |
| Total Amount (A) | A = P + SI (simple) or A = P + CI (compound) |
| Compounding Frequency | If compounded n times per year: A = P × (1 + r/(100n))^(n×t) |
| Annual Equivalent Rate (EAR) | EAR = (1 + r/(100n))^n – 1 |
| Rule of 72 | Rough estimate of doubling time: Doubling Time ≈ 72 / r (rate expressed as a percentage). |
| Effective Interest for Partial Years | Use t as a fraction; e.g., 6 months = 0.5 years. |
| VAT / Taxes | Not considered in basic calculations. |
| Common Mistakes | Forgetting to divide r by 100, using wrong compounding frequency, rounding too early. |
3. Worked Example
Problem
An investor deposits ₹50,000 in a bank that offers 8 % p.a. interest compounded quarterly. The money stays in the account for 3.5 years.
Questions:
- What is the amount after 3.5 years?
- What is the total interest earned?
Solution
| Step | Calculation | Result |
|---|---|---|
| 1. Identify variables | P = ₹50,000, r = 8 %, n = 4 (quarterly), t = 3.5 years | |
| 2. Use compound interest formula | A = P × (1 + r/(100n))^(n×t) |
|
| 3. Plug in numbers | A = 50,000 × (1 + 8/(100×4))^(4×3.5) |
|
| 4. Compute inside parentheses | 1 + 8/(400) = 1 + 0.02 = 1.02 |
|
| 5. Compute exponent | 4 × 3.5 = 14 |
|
| 6. Raise to the power | 1.02^14 ≈ 1.312 (use calculator) |
|
| 7. Multiply by principal | A ≈ 50,000 × 1.312 = ₹65,600 |
|
| 8. Total interest | CI = A – P = 65,600 – 50,000 = ₹15,600 |
Answer
- Amount after 3.5 years: ₹65,600
- Total interest earned: ₹15,600
Quick Check (Using Rule of 72)
- Approx. doubling time:
72 / 8 ≈ 9years. - 3.5 years < 9 → amount should be < double → ₹65,600 < ₹100,000 ✔️
4. Quick Revision Summary
| Concept | Formula | Notes |
|---|---|---|
| Simple Interest | SI = (P × r × t) / 100 |
Linear growth. |
| Total Amount (Simple) | A = P + SI |
|
| Compound Interest | CI = P × (1 + r/100)^t – P |
Exponential growth. |
| Total Amount (Compound) | A = P × (1 + r/100)^t |
|
| Compounded n times a year | A = P × (1 + r/(100n))^(n×t) |
n = 1 (annual), 12 (monthly), etc. |
| Effective Annual Rate | EAR = (1 + r/(100n))^n – 1 |
Compare different rates. |
| Rule of 72 | Doubling Time ≈ 72 / r |
Quick mental estimate. |
Tip for Patwari / Lekhpal Exam
- Always convert the rate to a decimal before plugging into formulas.
- For quarterly, monthly, or other compounding, use the n‑times‑per‑year formula.
- When time is given in months, t = months / 12.
- Double‑check the exponent:
n × tmust reflect the total number of compounding periods.
Happy studying!