AdriAnne and Anna's Auto Repair wants to add a new service bay. How much can they borrow at an annual rate of 5%, compounded quarterly, if the desired quarterly payment is $6,100? Assume a loan period of 4.5 years. Round your answer to the nearest cent.
A)$107,355.83
B)$67,583.80
C)$97,780.25
D)$87,963.78
E)$77,900.37

Question

AdriAnne and Anna's Auto Repair wants to add a new service bay. How much can they borrow at an annual rate of 5%, compounded quarterly, if the desired quarterly payment is $6,100? Assume a loan period of 4.5 years. Round your answer to the nearest cent. ​
A)$107,355.83
B)$67,583.80
C)$97,780.25
D)$87,963.78
E)$77,900.37

Quizplus · Accepted Answer

To find the loan amount, use the formula for the present value of an annuity: $ PV = PMT \times \left(1 - (1 + r)^{-n}\right) / r $, where $ PMT = 6100 $, $ r = 0.05/4 $, and $ n = 4.5 \times 4 $. Calculating gives approximately $97,780.25.

AdriAnne and Anna's Auto Repair Wants to Add a New