Question

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.)
a.
7.03%
b.
13.21%
c.
11.27%
d.
6.97%

Answer 1

Monthly rate = 0.1127/12 = 0.0093916666667.
Number of payments = 2.5·12 = 30.

Monthly payment = 779·r / (1 − (1+r)^−30) ≈ $29.90 (rounded to the nearest cent).
Total paid on card = 29.90·30 = $897.00, so interest paid = 897.00 − 779.00 = $118.00.

Electricity over 6 years: 6·365 + 2 leap days = 2192 days, so cost = 2192·0.36 = $789.12.

Lifetime cost = 779.00 + 118.00 + 789.12 = $1686.12.

Percent of lifetime cost that was interest = 118.00 / 1686.12 ≈ 0.06998 ≈ 6.998% ≈ 6.97% (closest choice).

Answer: d. 6.97%