# Simple and Compound Interest Questions with Answers and Formulas

> Simple interest and compound interest formulas, the CI-SI difference shortcut, and solved questions with explanations for placement aptitude tests.

Source: https://www.sansal.in/aptitude/simple-and-compound-interest · Last updated: 2026-09-19 · How often it appears: High. Usually 1-2 questions, often the CI−SI difference shortcut.

Simple interest is linear, compound interest is exponential, and most questions test whether you know the difference precisely. The two-year difference shortcut alone answers a surprising share of the questions asked.

## Concepts

### Simple interest never earns on interest

Simple interest is computed on the original principal every single year, so the interest amount is identical each year. Compound interest adds each year's interest to the principal, so the base grows and so does the interest.

### The difference is small and predictable

Over two years, CI exceeds SI by exactly P(R/100)² — this is just the interest earned on the first year's interest. Memorise it; it converts a long question into one multiplication.

### Watch the compounding frequency

If interest compounds half-yearly, halve the rate and double the number of periods. Quarterly means quarter the rate and quadruple the periods. Questions frequently hide this in one word.

## Formulas

| Formula | Rule | Note |
| --- | --- | --- |
| Simple interest | SI = (P × R × T) / 100 |  |
| Amount under SI | A = P + SI |  |
| Compound amount | A = P × (1 + R/100)^T |  |
| Compound interest | CI = A − P |  |
| CI − SI over 2 years | Difference = P × (R / 100)² |  |
| CI − SI over 3 years | Difference = P × (R/100)² × (3 + R/100) |  |
| Half-yearly compounding | Use rate R/2 and time 2T |  |

## Worked examples

### Example 1

**Question:** Find the simple interest on ₹5,000 at 10% per annum for 2 years.

**Solution:**

1. SI = (P × R × T) / 100
2. = (5000 × 10 × 2) / 100
3. = 100000 / 100

**Answer:** ₹1,000

### Example 2

**Question:** Find the compound interest on ₹5,000 at 10% per annum for 2 years.

**Solution:**

1. A = P(1 + R/100)^T = 5000 × (1.1)²
2. = 5000 × 1.21 = ₹6,050
3. CI = A − P = 6050 − 5000

**Answer:** ₹1,050

**Check:** CI exceeds SI by ₹50, which matches the shortcut: P(R/100)² = 5000 × 0.01 = 50.

### Example 3

**Question:** The difference between compound and simple interest on a sum for 2 years at 10% is ₹60. Find the sum.

**Solution:**

1. Difference over 2 years = P × (R/100)²
2. 60 = P × (10/100)² = P × 0.01
3. P = 60 / 0.01

**Answer:** ₹6,000

## Practice questions

1. Simple interest on ₹8,000 at 5% per annum for 3 years is:
   - A. ₹1,000
   - B. ₹1,200
   - C. ₹1,400
   - D. ₹1,600
   - **Answer:** B. ₹1,200 — (8000 × 5 × 3) / 100 = ₹1,200.

2. The amount on ₹10,000 at 10% compound interest for 2 years is:
   - A. ₹11,000
   - B. ₹12,000
   - C. ₹12,100
   - D. ₹12,500
   - **Answer:** C. ₹12,100 — 10000 × (1.1)² = 10000 × 1.21 = ₹12,100.

3. The difference between CI and SI on ₹10,000 for 2 years at 5% is:
   - A. ₹20
   - B. ₹25
   - C. ₹30
   - D. ₹50
   - **Answer:** B. ₹25 — P(R/100)² = 10000 × (0.05)² = 10000 × 0.0025 = ₹25.

4. At what rate of simple interest will a sum double itself in 10 years?
   - A. 8%
   - B. 10%
   - C. 12%
   - D. 12.5%
   - **Answer:** B. 10% — To double, SI must equal P. P = (P × R × 10)/100 → 100 = 10R → R = 10%.

5. A sum of ₹4,000 at 10% per annum compounded half-yearly for 1 year amounts to:
   - A. ₹4,400
   - B. ₹4,410
   - C. ₹4,420
   - D. ₹4,440
   - **Answer:** B. ₹4,410 — Half-yearly: rate 5%, 2 periods. 4000 × (1.05)² = 4000 × 1.1025 = ₹4,410.

6. A sum triples in 20 years at simple interest. The rate is:
   - A. 5%
   - B. 8%
   - C. 10%
   - D. 15%
   - **Answer:** C. 10% — To triple, interest = 2P. 2P = (P × R × 20)/100 → 200 = 20R → R = 10%.

## Where marks get lost

- Using the compound formula but forgetting to subtract the principal to get CI.
- Ignoring half-yearly or quarterly compounding stated in the question.
- Applying the 2-year difference shortcut to a 3-year question.
- Treating "amount" and "interest" as the same thing.

## Related topics

- [Percentages](https://www.sansal.in/aptitude/percentages)
- [Profit & Loss](https://www.sansal.in/aptitude/profit-and-loss)
- [Ratio & Proportion](https://www.sansal.in/aptitude/ratio-and-proportion)

Practise these on Sansal: https://www.sansal.in/practice/aptitude