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 12​% over five years. Anderson expects its product sales to be slow during the first​ year, but to increase subsequently at an annual rate of 8​%. 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 8​% over the previous one. Determine the five annual payments

Answer 1

Solution :-

Rate of Interest ( r ) = 12%

Let First Payment be X

Growth Rate in Annuity ( g ) = 8%

Loan Amount = $130,000

Term ( n ) = 5

Now we need to take Loan amount as present Value of growing annuity

5,200 = X * 0.16626

X = $31,275.60

Therefore

1st Payment = $31,275.60

2nd Payment = $31,645.07 * ( 1 + 0.08 ) = $33,777.65

3rd Payment = $33,777.65 * ( 1 + 0.08 ) = $36,479.86

4th Payment = $36,479.86 * ( 1 + 0.08 ) = $39,398.25

5th Payment = $39,398.25 * ( 1 + 0.08 ) = $42,550.11

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