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 $130,000. Kersey will borrow money from a bank at an interest rate of 15% over five years. Anderson expects its product sales to be slow during the first year, but to increase subsequently at an annual rate of 6%. 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 6% over the previous one. Determine the five annual payments. Fill in the table below. (Round to the nearest dollar.) Period (M)Payment

Explanation / Answer

Lowest installment can be found using following formula

PV(growing annuity) = A[1-(1+g)^n(1+r)^-n/(r-g)]

130,000 = A[1-(1.06)^5(1.15)^-5 / 0.15-0.06]

130,000 = A [1-1.3382*0.4971 / 0.09]

=130,000 =A[1-0.66533/0.09]

=130,000=A(3.7185)

A = 34960.29$

Thus 1st payment = 34960.29$

2nd payment = 34960.29(1.06) = 37057.91$

3rd payment = 37057.91(1.06) = 39281.39$

4th payment = 39281.39(1.06) =41638.27$

5th payment = 41638.27(1.06) = 44136.57$

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