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.)
Answer
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.
Explanation
Use the monthly rate 0.1301 ÷ 12 and the loan-payment formula for each grill. The monthly payment is about $14.79 for Brand F over 60 months, or $887.40 total. Brand G’s payment is about $6.74 over 36 months; three grills require 108 payments, totaling $727.92. Brand G is cheaper by $887.40 − $727.92 = $159.48, so the correct choice is “Brand G will end up costing $159.48 less than Brand F.”
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