📚 Simple & Compound Interest – Study Notes
For the Andhra Pradesh Police Sub‑Inspector (SI) Exam – Quantitative Aptitude
1️⃣ What Is Interest?
| Type | Everyday Analogy | What It Means |
|---|---|---|
| Simple Interest (SI) | You borrow a book from a friend for a week. The extra pages you read during that week are like the extra “cost” (interest) you pay. | Interest is calculated only on the original amount (principal). |
| Compound Interest (CI) | You put a small seed in a pot. Each month it grows, and next month you grow from the new size, not just the original seed. | Interest is calculated on the original amount and on the interest that has already accumulated. |
Key Idea – Simple = no “interest on interest”.
Key Idea – Compound = interest keeps piling on itself.
2️⃣ Simple Interest (SI)
2.1 Formula
[ \text{SI} = \frac{P \times R \times T}{100} ]
- P = Principal (original amount)
- R = Rate of interest per year (in %)
- T = Time (in years)
2.2 Quick Calculation Steps
- Multiply P × R × T.
- Divide the product by 100.
- Result = SI.
2.3 Tiny Example
| P | R | T | Calculation | SI |
|---|---|---|---|---|
| ₹10,000 | 5% | 2 years | (10,000 \times 5 \times 2 = 100,000) | (100,000 ÷ 100 = ₹1,000) |
Answer – The interest after 2 years is ₹1,000.
3️⃣ Compound Interest (CI)
3.1 Formula (for total amount)
[ A = P \times \left(1 + \frac{R}{100}\right)^{T} ]
- A = Total amount (principal + interest)
- Other symbols same as above.
3.2 Getting Just the Interest
[ \text{CI} = A - P ]
3.3 Quick Calculation Steps
- Compute (\frac{R}{100}).
- Add 1 to that value → (1 + R/100).
- Raise the result to the power T.
- Multiply by P → gives A.
- Subtract P → gives CI.
3.4 Tiny Example
| P | R | T | Calculation | A | CI |
|---|---|---|---|---|---|
| ₹5,000 | 10% | 3 years | (5,000 \times (1+0.10)^3) | (5,000 \times 1.331 = ₹6,655) | (6,655 - 5,000 = ₹1,655) |
Answer – The interest after 3 years is ₹1,655.
4️⃣ Quick Comparison Cheat‑Sheet
| Feature | Simple Interest | Compound Interest |
|---|---|---|
| Interest on | Only the original amount | Original amount + accumulated interest |
| Formula | (PRT/100) | (P(1+R/100)^T) |
| Uses | Short‑term loans, savings with no compounding | Long‑term savings, investments, mortgages |
5️⃣ Common Exam Tips
| Tip | Why It Helps |
|---|---|
| Memorize the formulas exactly as written. | Saves time and avoids mistakes. |
| Convert all rates to the same time unit (e.g., yearly). | Keeps calculations consistent. |
| Work backwards – if you’re given total amount, subtract P to get CI. | Simplifies problems. |
| Check units – sometimes T is given in months; convert to years (divide by 12). | Prevents mis‑reading. |
| Use a calculator for powers ((1+R/100)^T). | Reduces errors in exponentiation. |
| Practice with small numbers first. | Builds confidence before tackling bigger values. |
6️⃣ Practice Questions (Try them)
| # | Question | Answer |
|---|---|---|
| 1 | A student borrows ₹8,000 at 6% per annum for 1.5 years. What is the simple interest? | ₹720 |
| 2 | A ₹12,000 deposit grows to ₹15,000 in 4 years at compound interest. What is the annual rate? | 6% (approx.) |
| 3 | ₹3,000 is invested at 8% compounded yearly for 2 years. What is the amount after 2 years? | ₹3,472.32 |
| 4 | If the total amount after 3 years is ₹4,500, and the principal was ₹3,000, what is the compound interest? | ₹1,500 |
Answer Key – Work through the formulas step by step; you’ll get the same results.
7️⃣ Summary
| Concept | Quick Takeaway |
|---|---|
| Simple Interest | “One‑time” interest on the original amount. |
| Compound Interest | “Interest on interest” – the amount grows faster over time. |
| Formulas |