Question

Anderson Manufacturing Co., a small fabricator of plastics, needs to purchase an extrusion molding machine for $150,000. They will borrow money from the bank at 7% interest over five years. Since they expect sales to be slow during the first year, but to increases at an annual rate of 10% a year, the company arranges with the bank to pay off the loan using a balloon scale" which results in the lowest payment at the end of the first year, and each subsequent payment will be 10% higher than the previous payment, what is the size of the LAST payment on the loan? A) $44,435 B) $30,350 C) $36,724 D) $40,396

Answer 1

A) $44,435

Explanation:

You want to know the amount of the last payment on a loan of $150,000 at 7% for 5 years, if annual payments increase at 10% per year.

Amortization

No doubt there is a formula for balloon scale payment amounts, but we haven't found it and don't feel inclined to derive it. Hence, we have solved this problem using the "goal seek" capability of a spreadsheet.

Formulating the spreadsheet to calculate interest at 7% per year and payment amounts increasing at 10% per year, the solver found that the final payment amount would be $44,435.

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Additional comment

This can be approximated by finding the annual payment assuming the loan is paid with constant payments. If this is considered to be the payment in the middle (3rd) year, then the final payment will be 1.10² times that amount, about 45,300. This estimate is sufficient to identify the correct answer choice among those offered. The calculation is shown in the second attachment.

(For longer loans, a different estimation method may be required.)

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