Franco purchased heavy machinery costing $95,000. The terms of the purchase were for monthly payments over 6 years at an interest rate of 6.5% compounded monthly. At the end of the 4^th year, Franco wanted to trade in this machinery for a newer model. Determine the balance owing on the old machinery at the end of year 4.

Question

Quizplus · Accepted Answer

To find the balance owing on the machinery at the end of year 4, we use the formula for the remaining balance of a loan, which is a function of the original loan amount, the interest rate, the total number of payments, and the number of payments made. The formula for the monthly payment (PMT) on a loan is derived from the formula for the present value of an annuity: PMT = [P * r * (1 + r)^n] / [(1 + r)^n - 1], where P is the principal amount ($95,000), r is the monthly interest rate (6.5% annual rate / 12 months = 0.00541667), and n is the total number of payments (6 years * 12 months = 72 payments). After calculating the monthly payment, we use the formula for the remaining balance (B) after a certain number of payments (m), which is B = [PMT * ((1 + r)^n - (1 + r)^m)] / [r * (1 + r)^n], where m is the number of payments made (4 years * 12 months = 48 payments). Plugging in the values and solving gives us the balance owing at the end of year 4, which matches option B, $35,849.11.

Franco Purchased Heavy Machinery Costing $95,000