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A man owes Rs. 800 dues in 2 years without interest and Rs. 300 dues in 9 years with a 6% annual effectiverate of interest. He wishes to pay these debts in two equal installments due 4 and 5 years hence, respectively. If money is worth 4% converted semiannually, how much should each instalment be?

Question

A man owes Rs. 800 dues in 2 years without interest and Rs. 300 dues in 9 years with a 6% annual effectiverate of interest. He wishes to pay these debts in two equal installments due 4 and 5 years hence, respectively. If money is worth 4% converted semiannually, how much should each instalment be?

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Solution

This problem involves the concept of time value of money. Here are the steps to solve it:

Step 1: Calculate the present value of the debts

The present value of the Rs. 800 due in 2 years without interest is Rs. 800 / (1 + 0.04)^2 = Rs. 737.46

The present value of the Rs. 300 due in 9 years with a 6% annual interest rate is Rs. 300 / (1 + 0.06)^9 = Rs. 168.35

Step 2: Add the present values of the debts

The total present value of the debts is Rs. 737.46 + Rs. 168.35 = Rs. 905.81

Step 3: Calculate the value of each installment

The man wants to pay the debt in two equal installments due 4 and 5 years hence. The present value of each installment is the total present value of the debts divided by the sum of the present value factors for 4 and 5 years.

The present value factor for 4 years is 1 / (1 + 0.04)^4 = 0.8227 The present value factor for 5 years is 1 / (1 + 0.04)^5 = 0.7903

The sum of the present value factors is 0.8227 + 0.7903 = 1.613

The value of each installment is Rs. 905.81 / 1.613 = Rs. 561.27

So, each installment should be approximately Rs. 561.27.

This problem has been solved

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