Question

You are currently paying $15 per month for gym membership. You are trying to decide whether it's worth it to cancel the membership and instead to buy a set of fancypants all-in-one exercise equipment for $678. You expect the set to have a useful life of 20 years. If the real rate of return on investments is anticipated to be 6.9% APR, what is the net benefit to you of buying the equipment?

Assume your membership is paid for the current month, so you'd be starting your membership savings at the end of the month.

Assume also that you won't get bored with your exercise equipment and derive no utility from exercising with others. :)

Answer 1

Net benefit of buying equipment = present value of membership fee - cost of equipment

present value of membership fee is calculated using PV function in Excel :

rate = 6.9%/12 (converting annual rate into monthly rate)

nper = 240 (total number of months during 20-year period = 20 * 12 = 240)

pmt = -15 (Monthly fee. This is entered with a negative sign because it is a payment)

PV is calculated to be $1,949.80

A1 x fc C =PV(6.9%/12,240,-15) D E F B A $1,949.80 1

Net benefit of buying equipment = present value of membership fee - cost of equipment

Net benefit of buying equipment = $1,949.80 - $678

Net benefit of buying equipment = $1,271.80