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loan is to be returned in two equal yearly instalments. If the rate of interest is 10% p.a.. compounded annually and each
instalment is Rs6534, then the total interest charged (in Rs)is:
1642
1579
1728
1867
- Let's break this down by calculating how much of the principal is repaid through the instalments.
- We're given an annual interest rate of 10%, compounded annually.
- Each instalment is Rs 6534.
- Use the formula for the present value of an annuity to find the original loan amount (P):
$$
P = \frac{6534}{(1 + 0.10)^1} + \frac{6534}{(1 + 0.10)^2}
- Once calculated, this gives us the principal that was initially borrowed.
- To find the total interest, subtract the principal from the total paid in the two instalments.
- Let's calculate:
- First, find the present value of each instalment:
- \( \frac{6534}{1.10} = 5940 \)
- \( \frac{6534}{1.1^2} = 5400 \)
- Sum these values for the principal amount:
- \( 5940 + 5400 = 11340 \)
- Total loan repayment = \(6534 \times 2 = 13068\)
- Interest charged = Total loan repayment - Principal = \(13068 - 11340 = 1728\)
- Correct Answer: Option 3: 1728
By: santosh ProfileResourcesReport error
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