A customer is considering taking out a loan to purchase a piece of furniture. Th

Question

A customer is considering taking out a loan to purchase a piece of furniture. The store manager will offer as “a special favor” a loan to the customer for the purchase of the furniture. The terms of the loan are as follows: the rate will be 10% per year, and because the desk costs $600, the interest will come to $60 for the one-year loan. Thus, the total price is $660, and the customer can pay it off in 12 instalments of $55 each.

Using the interest rate of 10% per year, calculate the net present value of the loan – be sure you convert the interest rate to a monthly percentage! Based on this value, should the customer accept the terms of the loan?

This time, look at the loan from the store manager’s perspective. Again using an interest rate of 10% per year, what is the net present value of the loan from the store manager’s perspective?

If we instead assume an interest rate of 18%, keeping the payments at $55 per month, what is the net present value of the loan to the manager? What does this imply about the real rate of interest that the customer is being charged?

Explanation / Answer

Solution:-

Monthly effective interest rate = (1.10)1/12 = 0.79742 %

Net present value of loan :-

PVAF @0.79742% for 12 month = 11.40

Net present value = 11.40 * 55 = 627

Monthly int rate of 18% = (1.18)1/12 = 1.3888645%

PVAF = 10.9833987

Net Present value = 55*10.9833987 = 604.0869

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