A man invested his savings at the rate of 15\% per annum for two years at simple interest (SI). If he had invested the same amount at the rate of 20\% per annum for two years at compound interest (CI), compounded annually, he would have earned Rs. 280 more as interest. What is the amount of his savings?

Question

Accepted Answer

**Solution:**

1. Let the principal amount be $ P $.

2. Calculate the simple interest (SI) for 2 years at 15\% per annum:
   $$
 $  \text{SI} = \frac{P \times 15 \times 2}{100} = \frac{30P}{100} = 0.3P$
   $$

3. Calculate the compound interest (CI) for 2 years at 20\% per annum, compounded annually:
   $$
  $ \text{Amount} = P \times \left(1 + \frac{20}{100}\right)^2 = P \times (1.2)^2 = P \times 1.44$
   $$
   $$
 $  \text{CI} = \text{Amount} - P = 1.44P - P = 0.44P$
   $$

4. According to the problem, the difference between CI and SI is Rs. 280:
   $$
   0.44P - 0.3P = 280
   $$
   $$
   0.14P = 280
   $$

5. Solve for $ P $:
   $$
 $  P = \frac{280}{0.14} = 2000$
   $$

**Answer:** Rs. 2000

Answer

Answer

Answer

Answer