Anderson Manufacturing Co., a small fabricator of plastics, needs to purchase an

Question

Anderson Manufacturing Co., a small fabricator of plastics, needs to purchase an extrusion molding machine for $180,000. Kersey will borrow money from a bank at an interest rate of 5% over five years. Anderson expects its product sales to be slow during the first year, but to increase subsequently at an annual rate of 9%. Anderson therefore arranges with the bank to pay off the loan on a "balloon scale," which results in the lowest payment at the end of the first year and each subsequent payment being just 9% over the previous one. Determine the five annual payments. Fill in the table below. (Round to the nearest dollar.) Period (N) Payment

Explanation / Answer

Loan = 180,000

Future value of the loan at the end of 5 years = PV*(1+r)^n = 180,000*(1+0.05)^5 = 229,730.68

The amount of 229,730.68 will be paid in 5 installemts with an increase of 9% each year

Let the lowest amount be x:

x + 1.09x + 1.09^2x 1.09^3x + 1.09^4x = 229,730.68

x + 1.09x + 1.1881x + 1.295029x + 1.41158x = 229,730.68

5.98471061x = 229,730.68

x = 38,386.26

1st annual payment = $38,386.26

2nd annual payment = 38,386.26*1.09 = $41,841.03

3rd annual payment = 41,841.03*1.09 = $45,606.72

4th annual payment = 45,606.72*1.09 = $49,711.32

5th annual payment = 49,711.32*1.09 = $54,185.34

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