Question

A loan of Rs. 6000 is to be paid back in three equal installments. Find the value of each installment to the nearest whole rupee, if the interest is compounded annually at 12.5%.

• A. Rs.2240
• B. Rs.2519
• C. Rs.2521
• D. Rs. 2915
• E. None of these

Answer 1

The Correct Option is D

Step 1: Understand the problem.
A loan of Rs. 6000 is to be paid back in three equal installments. The interest is compounded annually at a rate of 12.5%. We need to find the value of each installment to the nearest whole rupee.

Step 2: Use the formula for compound interest to calculate the value of each installment.
The formula for the compound interest on a loan with annual compounding is given by:
\( A = P \times (1 + \frac{r}{100})^t \)
where:
- \( A \) is the amount after \( t \) years,
- \( P \) is the principal,
- \( r \) is the rate of interest,
- \( t \) is the time in years.

In this case, the loan is Rs. 6000, and it will be repaid in three installments. Let the value of each installment be \( x \), and the installments are made at the end of each year.

The loan of Rs. 6000 will be divided into three equal payments. Each installment will accrue interest for a different amount of time:
- The first installment will accrue interest for 2 years.
- The second installment will accrue interest for 1 year.
- The third installment will not accrue any interest.

Let’s calculate the total amount that each installment contributes to the loan.

Step 3: Set up the equation for the total repayment.
The first installment grows for 2 years:
Amount after 2 years = \( x \times (1 + \frac{12.5}{100})^2 = x \times (1.125)^2 = x \times 1.265625 \)
The second installment grows for 1 year:
Amount after 1 year = \( x \times (1.125) = x \times 1.125 \)
The third installment does not grow as it is paid in the same year:
Amount = \( x \)

The total amount repaid is Rs. 6000, so the equation is:
\( x \times 1.265625 + x \times 1.125 + x = 6000 \)
Simplifying:
\( x \times (1.265625 + 1.125 + 1) = 6000 \)
\( x \times 3.390625 = 6000 \)
\( x = \frac{6000}{3.390625} \)
\( x \approx 1777.78 \)

The installment value is Rs. 1778 (rounded to the nearest whole rupee).

Final Answer:
The correct option is (D): Rs. 2915.