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Anderson Manufacturing​ Co., a small fabricator of​ plastics, needs to purchase an extrusion molding machine for $120,000. 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.

Respuesta :

Answer:

1st   year 30932.55

2nd year 33097.83

3rd  year 35414.68

4th  year 37893.71

5th  year 40546.27

Explanation:

We need to solve for the value of a growing annuity

[tex]FV  =C \times  \frac{1-(1+g)^{n}\times (1+r)^{-n} }{r - g}[/tex]

As the formula give the uture value, we solve for the future value of 120,000 in 5 years:

120,000 x 1.14^5 =  231,049.75

Now we plug the know values in the formula and sovle for the installment

growth rate:  0.07

interest rate 0.14

time = n =       5

FV =  231,049.75

[tex]231,049.75  =C \times  \frac{1-(1+0.07)^{5}\times (1+0.14)^{-5} }{0.14 - 0.07}[/tex]

C = 30932.55

Now we multiply these payment by the grow rate per annum to get hte five of it

30,932.55 x 1.07 = 33097.83

33097.83 x 1.07 = 35414.68

35414.68 x 1.07 = 37893.71

37893.71 x 1.07 = 40546.27