27
QuizMultiple Choice

Long Term Purchases

Question 27 • 26-27 Ignite Technical Math-Financial Math - MA2007

Seth has just decided to replace his computer. His old computer cost him $1,433 when he bought it exactly seven years ago. Seth paid for it with his credit card, which has an APR of 11.70%, compounded monthly. He made no other purchases with the card and paid off his balance after two and a half years of making identical monthly payments. The computer consumed about $0.79 of electricity every day. In total, what percentage of the lifetime cost of the computer did the electricity make up? (Assume that two out of the seven years were leap years, and round all dollar values to the nearest cent.)

Answer
A
82.157%
B
58.500%
C
21.718%
D
54.898%

Explanation

The monthly interest rate is 11.70% ÷ 12 = 0.975%, and Seth made 30 identical payments. Using the loan-payment formula, each payment is about $55.32, so the total paid for the computer was about 30 × $55.32 = $1,659.60. Over seven years, including two leap years, electricity cost 2,557 × $0.79 = $2,020.03; therefore, electricity was about $2,020.03 ÷ ($1,659.60 + $2,020.03) × 100% = 54.9% of the lifetime cost. The closest choice is 54.898%.

AI-written and checked against the verified answer.

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