A Xerox DocuColor photocopier costing $42,000 is paid off in 60 monthly installments at 6.5% APR. After three years the company wishes to sell the photocopier. What is the minimum price for which they can sell the copier so that they can cover the cost of the balance remaining on the loan?

Question

Quizplus · Accepted Answer

The monthly payment can be calculated using the formula for the monthly payment on a loan:

P = (r * A) / (1 - (1+r)^(-n))

where P is the monthly payment, A is the principal amount (in this case, $42,000), r is the monthly interest rate (which is the annual percentage rate divided by 12), and n is the number of months of the loan.

Plugging in the numbers gives:

P = (0.065/12 * 42000) / (1 - (1+0.065/12)^(-60))

P ≈ $865.66

After 36 months (three years), the remaining balance on the loan can be calculated using the formula for the present value of an annuity:

B = P * ((1 - (1+r)^(-t)) / r)

where B is the balance remaining on the loan after t months, P is the monthly payment, r is the monthly interest rate, and t is the number of months remaining on the loan.

Plugging in the numbers gives:

B = 865.66 * ((1 - (1+0.065/12)^(-24)) / (0.065/12))

B ≈ $18,448.18

Therefore, the minimum price for which the company can sell the photocopier and cover the balance remaining on the loan is $18,448.18. The answer is choice C.

A Xerox DocuColor Photocopier Costing $42,000 Is Paid Off in 60