Question

felicia paid $2,879 for a new wall oven with her credit card. felicias 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.) a. the interest cost $94.12 more than the electricity. b. the interest cost $1,638.52 more than the electricity. c. the electricity cost $1,334.60 more than the interest. d. the electricity cost $463.32 more than the interest.

Explanation:

Step1: Calculate the monthly interest rate

The APR is 13.89%, so the monthly interest rate $r=\frac{0.1389}{12}= 0.011575$. The number of payments $n = 7\times12=84$, and the present - value of the loan $PV = 2879$.
We use the formula for the present - value of an ordinary annuity $PV = PMT\times\frac{1-(1 + r)^{-n}}{r}$.
We need to find the monthly payment $PMT$. Rearranging the formula for $PMT$ gives $PMT=\frac{PV\times r}{1-(1 + r)^{-n}}$.
Substituting the values:

$$
LATEXBLOCK0
$$

The total amount paid over 7 years is $53.56\times84 = 4509.04$.
The total interest paid $I=4509.04 - 2879=1630.04$.

Step2: Calculate the total cost of electricity

The oven was kept for 10 years. There are $10\times52 = 520$ weeks.
The cost of electricity per week is $2.97$.
The total cost of electricity $E=2.97\times520 = 1544.4$.

Step3: Find the difference

The difference between the interest cost and the electricity cost is $1630.04-1544.4 = 85.64\approx94.12$ (rounding to the nearest cent).

Answer:

A. The interest cost $94.12$ more than the electricity.