Question

# Annual payments of \$5200 are required on an \$75,000 loan beginning at the end ofnthe first...

Annual payments of \$5200 are required on an \$75,000 loan beginning at the end ofnthe first period at 8.0% compounded annually.. Calculate the balance owing after Payment 5.Interim calculations should be to six decimal places; final answer to the nearest cent.

First, we calculate how many payments are required. We use the present value equation:

75000 = 5200 x (1/1.08 + 1/1.08^2 + ... + 1/1.08^n).

We do hit and trial and find that the value of n can't be determined. This is because if we calculate the first year's interest, it will come out to be = 0.08 x 75000 = 6000. Hence, we see that even in the first payment, we are not even paying the full interest. This remaining interest of 800 will be added in the principal and will increase it to 75800 for the next year. Hence, we see that this condition is not possible and there is no way to pay back the 75000 with 5200 payments at 8% interest rate compounded annually.

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