Question

You have a loan outstanding. It requires making 6 annual payments at the end of the next 66
years of $8,000 each. Your bank has offered to allow you to skip making the next 5th payments in lieu of making one large payment at the end of the​ loan's term in 6 years. If the interest rate on the loan is 8.16 %, what final payment will the bank require you to make so that it is indifferent between the two forms of​ payment?

Answer 1

Answer on Question #79025 – Math – Financial Math

Question

You have a loan outstanding. It requires making 6 annual payments at the end of the next 66 (In my opinion this is a mistake. The value should be equal to 6) years of $8,000 each. Your bank has offered to allow you to skip making the next 5th payments in lieu of making one large payment at the end of the loan's term in 6 years. If the interest rate on the loan is 8.16 %, what final payment will the bank require you to make so that it is indifferent between the two forms of payment?

Solution

In order for both forms of payment to be the same the present value of all cash flow for 6 annual payments (PV₁₋₆) should be equal to present value of one large payment (PV).

Let's find present value of all cash flows for 6 annual payments. The calculation is shown in table form.

Formula for final payment:

$$PV = 36804.21083 = \frac{CF6}{(1+0.0816)^6}$$

, therefore

$$CF6 = 36804.21083 * (1+0.0816)^6 = 58924.72731$$

Answer: 58924. 72731

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