Mike's Sporting Goods sells elliptical trainers under two payment plans: cash and installment. Under the installment plan, the customer pays $90/month over 5 years with interest changed on the balance at a rate of 19%/year compounded monthly. Find the cash price for an elliptical trainer if it is equivalent to the price paid by a customer using the installment plan. Round your answers to two decimal places.
A) $3,469.47
B) $3,452.28
C) $3,464.42
D) $3,492.47
E) $3,502.80

Question

Mike's Sporting Goods sells elliptical trainers under two payment plans: cash and installment. Under the installment plan, the customer pays $90/month over 5 years with interest changed on the balance at a rate of 19%/year compounded monthly. Find the cash price for an elliptical trainer if it is equivalent to the price paid by a customer using the installment plan. Round your answers to two decimal places. ​
A) $3,469.47
B) $3,452.28
C) $3,464.42
D) $3,492.47
E) $3,502.80

Quizplus · Accepted Answer

We can use the present value formula to find the cash price equivalent to the installment plan payments. Let P be the cash price we want to find.

PV = (C/r) * [1 - (1+r)^(-n)],

where C is the monthly payment, r is the monthly interest rate (19%/12 = 1.58%), n is the number of months (5 years * 12 months/year = 60), and PV is the present value.

Substituting the values, we get:

P = PV = (90/1.005^60) * [1 - (1.005)^(-60)]/0.0158
P ≈ $3,469.47

Therefore, the best choice is A.

Mike's Sporting Goods Sells Elliptical Trainers Under Two Payment Plans