Question

Anderson Manufacturing​ Co., a small fabricator of​ plastics, needs to purchase an extrusion molding machine for ​$180 comma 000. Kersey will borrow money from a bank at an interest rate of 14​% over five years. Anderson expects its product sales to be slow during the first​ year, but to increase subsequently at an annual rate of 7​%. 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 7​% over the previous one. Determine the five annual payments.

Answer 1

Answer:

1st     46,398.83

2nd    49,646.74

3rd      53,122.02

4th      56,840.56

5th       60,819.40

Explanation:

given a growing annuity we have to solve for the installement

$FV = \frac{1-(1+g)^{n}\times (1+r)^{-n} }{r - g}$

FV = PV (1+r)^5 = 180,000 x 1.14^5 =  346,574.62  

grow rate 0.07

interest rate 0.14

n = time     5

$346,574.62 = C \times \frac{1-(1+0.07)^{5}\times (1+0.14)^{-5} }{0.14 - 0.07}$

C = 46398.8284

Now, to determiante the subsequent payment we multiply by the grow rate of 1.07