Question

You are considering buying one of two brands of barbecue grills. Brand F costs $650 and will last for about fifteen years. Brand G costs $200 and will last for about five years, so you will need to buy three of them over the years to equal one Brand F grill. In either case, you plan to pay for the grill with your credit card, which has an interest rate of 13.01%, compounded monthly. You will pay off a Brand F grill in five years of monthly payments, and you will pay off a Brand G grill in three years of monthly payments. Assuming that you have no other purchases on your credit card, over a fifteen-year period, which kind of grill will be cheaper, and how much cheaper will it be? (Round all dollar values to the nearest cent.)
a.
Brand G will end up costing $159.48 less than Brand F.
b.
Brand G will end up costing $50.00 less than Brand F.
c.
Brand F will end up costing $134.28 less than Brand G.
d.
Brand F will end up costing $91.08 less than Brand G.


Please select the best answer from the choices provided

A
B
C
D

Answer 1

A

Work (outline):
- Monthly rate = 0.1301/12 = 0.010841666666666667.
- Monthly payment formula: PMT = P * i / (1 - (1+i)^(-n)).
- Brand F: P = 650, n = 60 → PMT_F ≈ $14.79790, total paid = 60·PMT_F ≈ $887.57.
- Brand G: P = 200, n = 36 → PMT_G ≈ $6.73541, total per grill = 36·PMT_G ≈ $242.52; three grills over 15 years total ≈ 3·$242.52 = $727.04.
- Difference: $887. (F) − $727. (G) ≈ $159.48, so Brand G is cheaper by $159.48.

Thus choice (a) is correct.