You are planning to buy one of two brands of sofas, which you hope to use over the next twenty years. Brand J costs $975 and lasts for about twenty years. Brand K costs $265 and lasts for about five years, so you will need to buy four Brand K sofas to equal one Brand J sofa. In either case, you plan to pay for your sofa using your credit card, which has an interest rate of 14.55%, compounded monthly. You can pay off a Brand J sofa with eight years of monthly payments, and you can pay off a Brand K sofa with three years of monthly payments. Assuming that you make no other purchases on your credit card, over twenty years, which brand will be cheaper, and how much cheaper will it be? (Round all dollar values to the nearest cent.)
Answer
A
Brand J will be $591.36 cheaper than Brand K.
B
Brand J will be $85.00 cheaper than Brand K.
C
Brand K will be $1,132.23 cheaper than Brand J.
D
Brand K will be $340.32 cheaper than Brand J.
Explanation
Use the monthly rate, 14.55% ÷ 12 = 1.2125%, to calculate each loan’s fixed monthly payment. Financing Brand J for 96 months gives payments of about $17.24, or about $1,654.75 total. Financing one Brand K sofa for 36 months gives payments of about $9.13; four sofas cost about $1,314.43 in payments altogether. Brand K is therefore cheaper by about $1,654.75 − $1,314.43 = $340.32, matching “Brand K will be $340.32 cheaper than Brand J.”
AI-written and checked against the verified answer.