Simple & Compound Interest
Quantitative Aptitude – Himachal Pradesh PSC
Goal: Know what the terms mean, how to find the amounts, and be ready for exam questions.
1. Quick Overview
| Term | What it means | When you see it |
|---|---|---|
| Simple Interest (SI) | Extra money earned on the original amount only. | “Simple interest on ₹10,000 for 2 years at 5%.” |
| Compound Interest (CI) | Extra money earned on the original amount plus on the interest that has already accumulated. | “Compound interest on ₹10,000 for 2 years at 5% p.a., compounded annually.” |
Analogy
Think of a plant:
Simple – you water it once, it grows, but you never water the new leaves again.
Compound – you water the plant, then you water the leaves it just grew, so it grows faster.
2. Simple Interest (SI)
2.1 Definition
SI is the interest charged on the principal (original sum) only.
2.2 Formula
SI = (Principal × Rate × Time) / 100
- Principal (P) – the money borrowed or invested.
- Rate (R) – interest rate per year (in %).
- Time (T) – number of years.
2.3 Steps to calculate
- Write down P, R, T.
- Multiply P × R × T.
- Divide by 100 to account for the percent.
2.4 Tiny Example
| P | R | T | SI |
|---|---|---|---|
| ₹5,000 | 6% | 3 years | (5,000 × 6 × 3) ÷ 100 = ₹900 |
Total amount after 3 years = Principal + SI = ₹5,900.
3. Compound Interest (CI)
3.1 Definition
CI is the interest earned on the principal and on the interest that has been added in previous periods.
3.2 Formula
CI = Principal × ( (1 + R/100) ^ n ) - Principal
- n = number of compounding periods (e.g., if interest is compounded every year, n = T).
3.3 Steps to calculate
- Compute
R/100(e.g., 5% → 0.05). - Add 1 to it:
1 + R/100. - Raise that to the power of n (
^n). - Multiply by the principal.
- Subtract the principal to get only the interest.
3.4 Tiny Example
| P | R | n | CI |
|---|---|---|---|
| ₹5,000 | 5% | 2 years | 5,000 × (1 + 0.05)^2 – 5,000 = 5,000 × 1.1025 – 5,000 = ₹512.50 |
Total amount after 2 years = ₹5,512.50.
4. When Interest Is Compounded More Than Once a Year
| Compounding Frequency | Formula (Annual Rate R) |
|---|---|
| Semi‑annually | P × (1 + R/(2×100))^(2T) |
| Quarterly | P × (1 + R/(4×100))^(4T) |
| Monthly | P × (1 + R/(12×100))^(12T) |
T= number of years.- The idea: split the yearly rate into equal parts for each period.
5. Quick Comparison
| Feature | Simple Interest | Compound Interest |
|---|---|---|
| Uses only | Principal | Principal + accumulated interest |
| Formula | Easy multiplication | Exponentiation |
| Growth | Linear | Exponential |
| Time Effect | Less impact | More impact over long periods |
Tip: For short times or low rates, the difference is small; for long times or high rates, CI grows much faster.
6. Common Pitfalls
| Mistake | Fix |
|---|---|
| Using T = months directly in SI formula | Convert months to years: T = months ÷ 12. |
| Forgetting to divide by 100 in the rate | Always convert percent to decimal before calculations. |
Mixing up n (number of periods) with T (years) |
Remember: n = compounding periods per year × T. |
| Adding principal twice in CI | Only subtract the principal once to get the interest. |
7. Sample PSC‑Style Questions
1. A person borrows ₹20,000 at 10% per annum simple interest for 4 years. What is the total amount payable?
Answer:
SI = (20,000 × 10 × 4) ÷ 100 = ₹8,000.
Total = 20,000 + 8,000 = ₹28,000.
2. ₹12,000 is deposited in a bank account that pays 6% per annum compounded semi‑annually. Find the amount after 3 years.
Answer:
n = 2 × 3 = 6 periods.
Amount = 12,000 × (1 + 0.06/2)^6 = 12,000 × (1.03)^6 ≈ ₹15,680.
3. Find the monthly rate of interest if the annual rate is 12% compounded monthly.
Answer:
Monthly rate = 12% ÷ 12 = 1% per month.