Question

A machine was purchased for $125,000. The down payment was $15,000, and the balance will be paid in 36 equal monthly payments, including monthly effective interest at 1.75%.

a) What is the amount of the monthly payment if the first payment is due one month from the date of the purchase?

b) What is the future value of the payments when completed, assuming a salvage value of $5,000 for the machine at the end of the payments.

Answer 1

Loan amount ($) = Purchase price - Down payment = 125,000 - 15,000 = 110,000

(a) Monthly payment ($) = Loan amount / P/A(1.75%, 36) = 110,000 / 26.5428** = 4,144.25

(b) Future value ($) = 4,144.25 x F/A(1.75%, 36) - 5,000 = 4,144.25 x 49.5661** - 5,000 = 205,414.43 - 5,000 = 200,414.43

**P/A(r%, N) = [1 - (1 + r)^-N] / r

P/A(1.75%, 36) = [1 - (1.0175)^-36] / 0.0175 = (1 - 0.5355) / 0.0175 = 0.4645 / 0.0175 = 26.5428

**F/A(r%, N) = [(1 + r)^N - 1] / r

F/A(1.75%, 36) = [(1.0175)³⁶ - 1] / 0.0175 = (1.8674 - 1) / 0.0175 = 0.8674 / 0.0175 = 49.5661