Charlie's Construction Co. acquired a new $800,000 backhoe on April 1, 2014. Charlie's will make six annual payments based upon 8% interest compounded annually, starting on March 31, 2015. How much will each payment be?
A) $504,136
B) $173,052
C) $160,234
D) $109,052

Question

Quizplus · Accepted Answer

The payments can be calculated using the formula for the present value of an annuity because Charlie's Construction Co. is essentially taking out a loan that it will pay back in equal annual installments. The formula is P = PMT * [(1 - (1 + r)^-n) / r], where P is the present value of the loan ($800,000), PMT is the annual payment, r is the annual interest rate (0.08), and n is the number of payments (6). Rearranging the formula to solve for PMT gives PMT = P / [(1 - (1 + r)^-n) / r]. Plugging in the numbers gives PMT = $800,000 / [(1 - (1 + 0.08)^-6) / 0.08], which calculates to approximately $173,052.