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.

Answer 1

The cash equivalent price of the similar instalment payment can be caudated by the PV of the series annuity payment as follows

PV of annuity = PMT * ( 1-(1+r) ^-n / r )

We have monthly payments = 90

Time = 12 payment *5 years = 60 pmt s

Rate = 19% pa

So

Cash equival price = 90 * ( 1-(1+0.19/12) ^-60 / 0.19/12 )

So

Cash price = $ 3469.47

Thanks