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?

Options

A. ₹ 9900
B. ₹ 10092
C. ₹ 11000
D. ₹ 11052

Answer

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

**Step 1: Identify the variables**
- Principal (P) = Rs. 7500
- Rate of interest (R) = 16% per annum
- Time (T) = 2 years

**Step 2: Use the compound interest formula**
The formula for compound interest is:

\[ A = P \left(1 + \frac{R}{100}\right)^T \]

Where:
- \(A\) is the total amount after time \(T\),
- \(P\) is the principal amount,
- \(R\) is the rate of interest,
- \(T\) is the time in years.

**Step 3: Substitute the values into the formula**
Substituting the values we have:

\[ A = 7500 \left(1 + \frac{16}{100}\right)^2 \]

**Step 4: Simplify the expression**
Calculating \(1 + \frac{16}{100}\):

\[ 1 + \frac{16}{100} = 1 + 0.16 = 1.16 \]

Now substitute this back into the equation:

\[ A = 7500 \times (1.16)^2 \]

**Step 5: Calculate \((1.16)^2\)**
Calculating \((1.16)^2\):

\[ (1.16)^2 = 1.3456 \]

**Step 6: Calculate the total amount**
Now, substitute this value back into the equation:

\[ A = 7500 \times 1.3456 \]

Calculating this gives:

\[ A = 10092 \]

**Step 7: Round the total amount**
Since currency is usually rounded to the nearest whole number, we can round Rs. 10092 to Rs. 10092.

Thus, the total amount to be paid at the end of 2 years is Rs. 10092.

### Final Answer:
The person has to pay Rs. 10092 at the end of 2 years to clear the loan.