# Anderson Manufacturing​ Co., a small fabricator of​ plastics, needs to purchase an extrusion molding machine for ​\$200,000. Kersey will borrow money from a bank at an interest rate of 13​% over five years. Anderson expects its product sales to be slow during the first​ year, but to increase subsequently at an annual rate of 11​%. 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 11​% over the previous one. Determine the five annual payments.（1,2,3,4,5）

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\$1.97 ONLY

The annual loan payments increasing at a rate of 11% shall form a growing annuity with growth rate of 11%. The annual payments shall be calculated in such a manner that the present value of all the five payments discounted at the interest rate of 13% shall add up to the loan amount.

Loan amount = \$200,000

Interest rate = r = 13% = 0.13

Growth rate = g = 11% = 0.11

Number of payments = n = 5

Let the first payment be P

Present value of growing annuity = P/(r-g) * {1 – (1+g/1+r)n}

\$200,000 = P/(0.13-0.11) * {1-(1.11/1.13)5}

\$200,000 = P/0.02 * (1-0.91458)

\$200,000 = P*4.27090

P = \$200,000/4.27090 = \$46,828.57

Hence, the first payment is \$46,828.57

The five annual payment shall be as below: