Question

Loan payments of $700 due three months ago and of $1000 due today are to be paid by a payment of $800 in two months and a final payment in five months. If 9% interest is allowed, and the focal date is five months from now, what is the amount of the final payment? The amount of each payment is $ (Round the final answer to the nearest cent as needed. Round all intermediate values to six decimal places as needed)​

Answer 1

Answer: $654.04

Step-by-step explanation:

We are given loan payments of $700 due three months ago and $1000 due today and we are to find the amount of the final payment to be paid by the borrower. Let the amount of the final payment be x.

The borrower is supposed to make a payment of $800 in two months from now. We need to determine the value of the final payment x such that all payments are settled.

To solve this problem, we use the time value of money formula. The formula is:

PV = FV / (1 + r)t

Where PV is the present value, FV is the future value, r is the interest rate, and t is the period.

We can write down the following equations based on the information given:

700/(1+0.09)^8 + 1000/(1+0.09)^5 + 800/(1+0.09)^3 + x/(1+0.09)^0 = 0

Simplifying the above equation we get:

x = $654.04

Therefore, the amount of the final payment will be $654.04.