A farmer borrowed 1,32,000 from a money lender to do cultivation in his field. The rate of interest is 12.5% per annum compounded annually. At the end of two years, he cleared his loan by paying 1,07,062.50 and his scooter. The cost in Rs ) of the scooter is:

Options

A. 75000
B. 45000
C. 60 000
D. 50000

Answer

To find the cost of the scooter, we first need to calculate the total amount the farmer needs to pay after borrowing Rs. 1,32,000 at a compound interest rate of 12.5% per annum for 2 years.

### Step 1: Calculate the total amount to be paid after 2 years using the compound interest formula.

The formula for compound interest is:
\[ A = P \left(1 + \frac{r}{100}\right)^n \]
where:
- \( A \) = the amount of money accumulated after n years, including interest.
- \( P \) = principal amount (the initial amount of money).
- \( r \) = annual interest rate (in percentage).
- \( n \) = number of years the money is borrowed for.

Here, \( P = 1,32,000 \), \( r = 12.5 \), and \( n = 2 \).

Substituting the values into the formula:
\[ A = 1,32,000 \left(1 + \frac{12.5}{100}\right)^2 \]
\[ A = 1,32,000 \left(1 + 0.125\right)^2 \]
\[ A = 1,32,000 \left(1.125\right)^2 \]
\[ A = 1,32,000 \times 1.265625 \]
\[ A = 1,67,062.50 \]

### Step 2: Determine the cost of the scooter.

The farmer cleared his loan by paying Rs. 1,07,062.50 and the cost of the scooter. Therefore, we can set up the equation:
\[ \text{Cost of the scooter} = \text{Total amount} - \text{Amount paid} \]
\[ \text{Cost of the scooter} = 1,67,062.50 - 1,07,062.50 \]
\[ \text{Cost of the scooter} = 60,000 \]

### Final Answer:
The cost of the scooter is Rs. 60,000.

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