A person took some loan from a bank at the rate of 15% annual interest. If he pays back Rs. 7,250 after 3 years then what is the amount of loan?

Question

Accepted Answer

To determine the amount of loan taken by the person, we need to calculate the principal amount based on the given interest rate and the total amount paid after 3 years. The problem states that the person pays back Rs. 7,250 after 3 years at an annual interest rate of 15%.

Let's use the formula for simple interest to find the principal amount (P):

$$ \text{Total Amount} = P + \text{Simple Interest} $$

The formula for simple interest (SI) is:

$$ \text{SI} = \frac{P \times R \times T}{100} $$

where:
- $ P $ is the principal amount,
- $ R $ is the rate of interest per annum (15% in this case),
- $ T $ is the time period in years (3 years here).

Given:
- Total Amount = Rs. 7,250
- Rate of Interest (R) = 15%
- Time (T) = 3 years

Substitute the values into the formula for total amount:

$$ 7,250 = P + \frac{P \times 15 \times 3}{100} $$

$$ 7,250 = P + \frac{45P}{100} $$

$$ 7,250 = P \left(1 + \frac{45}{100}\right) $$

$$ 7,250 = P \left(\frac{145}{100}\right) $$

$$ 7,250 = \frac{145P}{100} $$

To find $ P $, multiply both sides by 100 and divide by 145:

$$ P = \frac{7,250 \times 100}{145} $$

$$ P = \frac{725,000}{145} $$

$$ P = 5,000 $$

Therefore, the principal amount, or the amount of loan taken, is Rs. 5,000. This confirms that Option 1 is correct.

**Explanation for why other options are incorrect:**

- **Option 2 (Rs. 4,500):** If the principal were Rs. 4,500, the total amount after 3 years at 15% interest would be less than Rs. 7,250. Calculating it would give a total amount less than Rs. 7,250, thus making this option incorrect.

- **Option 3 (Rs. 6,500):** If the principal were Rs. 6,500, the total amount after 3 years at 15% interest would exceed Rs. 7,250. This would result in a total amount greater than Rs. 7,250, making this option incorrect.

- **Option 4 (Rs. 5,500):** Similarly, if the principal were Rs. 5,500, the total amount after 3 years at 15% interest would also exceed Rs. 7,250, making this option incorrect.

Thus, the correct answer is indeed Option 1, Rs. 5,000, as it is the only option that satisfies the conditions given in the problem.