Question

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.)
a.
82.157%
b.
58.500%
c.
21.718%
d.
54.898%

Answer 1

Monthly interest rate r = 0.117/12 = 0.00975. He paid the $1,433 over n = 2.5·12 = 30 months, so the monthly payment is
payment = 1433 · r / (1 − (1 + r)^−30).
Calculate (1 + r)^30 ≈ 1.33788446, so payment ≈ 1433·0.00975/(1 − 1/1.33788446) ≈ $55.38 (rounded to the nearest cent).
Total amount paid on the card = 55.38 · 30 = $1,661.40.

Electricity: days = 7·365 + 2 leap days = 2557 days, cost = 2557 · $0.79 = $2,020.03.

Lifetime cost = 1,661.40 + 2,020.03 = $3,681.43.
Electricity percentage = 2020.03 / 3681.43 ≈ 0.54898 = 54.898%.

Answer: (d) 54.898%.