Question

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.)
a.
59.17%
b.
18.48%
c.
66.99%
d.
37.77%

Answer 1

First find the electricity cost.
- Days = 9*365 + 2 leap days = 3287 days.
- Electricity = 3287*(\$0.19) = \$624.53 (nearest cent).

Now find the total paid on the credit card.
- APR = 16.84% ⇒ monthly rate r = 0.1684/12 = 0.0140333333.
- n = 4 years = 48 months. Monthly payment:
payment = P * r / (1 − (1+r)^(-n)) = 745*(0.0140333333) / (1 − (1.0140333333)^(-48)) ≈ \$21.44 (round to nearest cent).
- Total paid on card = \$21.44 * 48 = \$1,029.12.

Lifetime cost = total paid on card + electricity = \$1,029.12 + \$624.53 = \$1,653.65.

Percentage that electricity makes up = 624.53 / 1653.65 ≈ 0.3777 = 37.77%.

Answer: d. 37.77%