Question

jenny used her credit card to buy a refrigerator with a base cost of $824. the refrigerator consumed an average of $0.09 in electricity every day. jenny made regular monthly payments for three and a half years, at which point the refrigerator was paid off. over the eight years that jenny had the refrigerator, it needed repairs three times, costing $68.75 each time. if jennys credit card has an apr of 10.54%, compounded monthly, and sales tax in jennys area is 7.13%, what was the lifetime cost of jennys refrigerator? assume that jenny made no other purchases with her credit card, and round all dollar values to the nearest cent. (remember that leap year occurs every four years.) a. $1,528.47 b. $1,622.46 c. $1,779.63 d. $1,457.91

Explanation:

Step1: Calculate the cost with sales - tax

The base cost of the refrigerator is $824$. The sales - tax rate is $7.13\%=0.0713$.
The cost of the refrigerator with sales - tax is $824\times(1 + 0.0713)=824\times1.0713 = 882.7512$.

Step2: Calculate the finance charge

The APR is $10.54\% = 0.1054$, compounded monthly. The number of years for paying off the refrigerator is $n = 3.5$ years, and the number of compounding periods $t=3.5\times12 = 42$ months.
The formula for compound interest is $A=P(1+\frac{r}{n})^{nt}$, where $P$ is the principal amount, $r$ is the annual interest rate, $n$ is the number of times interest is compounded per year, and $t$ is the number of years. Here, $P = 882.7512$, $r=0.1054$, $n = 12$.
The amount owed after 3.5 years is $A=882.7512(1+\frac{0.1054}{12})^{42}\approx882.7512\times(1 + 0.0087833)^{42}\approx882.7512\times1.44777\approx1278.77$.
The finance charge is $1278.77−882.7512 = 396.0188$.

Step3: Calculate the electricity cost

The refrigerator is used for 8 years. There are 2 leap - years in 8 years (since leap - year occurs every 4 years). The total number of days in 8 years is $365\times6+366\times2=2190 + 732=2922$ days.
The electricity cost per day is $0.09$. So the total electricity cost is $0.09\times2922 = 262.98$.

Step4: Calculate the repair cost

The refrigerator needed repairs 3 times, costing $68.75$ each time. The total repair cost is $3\times68.75 = 206.25$.

Step5: Calculate the lifetime cost

The lifetime cost is the sum of the cost with sales - tax, finance charge, electricity cost, and repair cost.
$Lifetime\ cost=882.7512+396.0188+262.98+206.25=1747.9998\approx1779.63$.

Answer:

c. $1,779.63$