A person borrowed Rs. 7500 at 16% per annum compound interest. How much does he have to pay at the end of 2 years to clear the loan ?

Question

Accepted Answer

To determine the amount a person has to pay at the end of 2 years for a loan of Rs. 7500 at 16% per annum compound interest, we use the formula for compound interest:

$$ A = P \left(1 + \frac{r}{100}\right)^n $$

Where:
- $ A $ is the amount to be paid at the end of the period.
- $ P $ is the principal amount (Rs. 7500).
- $ r $ is the rate of interest (16%).
- $ n $ is the number of years (2).

Substituting the given values into the formula:

$$ A = 7500 \left(1 + \frac{16}{100}\right)^2 $$
$$ A = 7500 \left(1 + 0.16\right)^2 $$
$$ A = 7500 \times (1.16)^2 $$
$$ A = 7500 \times 1.3456 $$
$$ A = 10092 $$

Therefore, the amount to be paid at the end of 2 years is Rs. 10092, which corresponds to Option 2.

**Explanation for why Option 2 is correct:**
- The calculation above shows that using the compound interest formula with the given principal, rate, and time period results in an amount of Rs. 10092. This matches Option 2, confirming it as the correct answer.

**Explanation for why other options are incorrect:**
1. **Option 1: Rs. 9900** - This amount is less than the calculated amount of Rs. 10092. It does not account for the full effect of compounding at 16% over 2 years.
2. **Option 3: Rs. 11000** - This amount is more than the calculated amount of Rs. 10092. It overestimates the compound interest accrued over 2 years.
3. **Option 4: Rs. 11052** - Similar to Option 3, this amount exceeds the calculated amount of Rs. 10092, indicating an overestimation of the compound interest.

In conclusion, the correct amount to be paid at the end of 2 years is Rs. 10092, making Option 2 the correct choice.