Long Term Purchases Answers

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.)

Harriet used her credit card to buy a $779 laptop, which she paid off by making identical monthly payments for two and a half years. Over the six years that she kept the laptop, it cost her an average of $0.36 of electricity per day. Harriet’s credit card has an APR of 11.27%, compounded monthly, and she made no other purchases with her credit card until she had paid off the laptop. What percentage of the lifetime cost of the laptop was interest? (Assume that there were two leap years over the period that Harriet kept the laptop, and round all dollar values to the nearest cent.)

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Melissa used her credit card to buy a $745 refrigerator. She kept the refrigerator for exactly nine years, during which time it consumed an average of $0.19 of electricity every day. Melissa’s credit card has an APR of 16.84%, compounded monthly. Melissa paid off her refrigerator by making identical monthly payments for four years. If she made no other purchases with her card, what percentage of the lifetime cost of the refrigerator did the electricity make up? (Assume that two of the years were leap years, and round all dollar values to the nearest cent.)

Megan’s TV had a base price of $189 and the sales tax was 6.88%. Over the next four years, the TV consumed an average of $0.06 of electricity every day. It also needed repairs twice, costing $29 each time. After four years, Megan got a new TV. What was the lifetime cost of Megan’s TV? (Remember that one in every four years is a leap year.)

Gareth has just remodeled his kitchen and wants to buy one of two stand-alone freezers. Consider the following table, which displays the prices, electricity costs, and lifespans of the two freezers he is considering:BrandBrand RBrand SPrice$575$98Avg. Cost/Wk$3.17$4.54Lifespan10 years2 yearsNo matter which brand he chooses, Gareth will pay for the freezer on his credit card, which has an APR of 9.31%, compounded monthly. It takes Gareth eighteen months to pay off a Brand S freezer and four years to pay off a Brand R freezer. Assuming that Gareth makes no other purchases or payments with his credit card, over the next ten years, which brand of freezer will have a lower lifetime cost, and how much lower will it be? (Round all dollar values to the nearest cent.)

Esteban bought a new stove for $986 on his credit card. He used the stove for eleven years before replacing it. The stove cost him an average of $0.14 per day in electricity. Esteban had preventive maintenance done on the stove, costing $24.25 each year for the eleven years. Esteban’s credit card has an APR of 9.26%, compounded monthly. He paid off his balance by making identical monthly payments for five years. Sales tax in Esteban’s area is 8.22%. Assuming that Esteban made no other purchases or payments with his credit card, what was the lifetime total cost of the stove? (Assume that two of the years Esteban had the stove were leap years, and round all dollar values to the nearest cent.)

Douglas has a credit card with an interest rate of 11.05%, compounded monthly. He used his credit card to buy a new sofa, which cost $670 before the sales tax of 7.94%. Douglas paid off his balance by making equal monthly payments for three years. Assuming that he had no other purchases on his credit card, how much did Douglas pay in total for the sofa? (Round all dollar values to the nearest cent.)

Felicia paid $2,879 for a new wall oven with her credit card. Felicia’s credit card has an APR of 13.89%, compounded monthly. It took Felicia seven years of identical monthly payments to pay for her oven, and she made no other purchases with her card until it was paid off. Over the ten years that she kept the oven, it used an average of $2.97 per week in electricity. Between the electricity and the interest, which component of the lifetime cost of the oven was greater, and how much greater was it? (Round all dollar values to the nearest cent.)