jamie needs a new roof on her house. the cash cost is $3300. she decides to finance the project by paying…

jamie needs a new roof on her house. the cash cost is $3300. she decides to finance the project by paying 6.0% down, with the balance paid in 12 monthly payments of $267. a) what finance charge will jamie pay? b) what is the apr to the nearest half percent? click the icon to view the apr table. a) the finance charge is $102. b) the apr is %.

jamie needs a new roof on her house. the cash cost is $3300. she decides to finance the project by paying 6.0% down, with the balance paid in 12 monthly payments of $267. a) what finance charge will jamie pay? b) what is the apr to the nearest half percent? click the icon to view the apr table. a) the finance charge is $102. b) the apr is %.

Answer

Explanation:

Step1: Calculate the amount financed

The cash - cost of the roof is $3300. The down - payment is 6% of $3300. The amount financed $A$ is $(1 - 0.06)\times3300=0.94\times3300 = 3102$.

Step2: Calculate the total amount repaid

The monthly payment is $267$ and the number of payments $n = 12$. So the total amount repaid $T=267\times12 = 3204$.

Step3: Recall the formula for finance charge

The finance charge $FC$ is the total amount repaid minus the amount financed. We already know from part (a) that $FC = 3204-3102=102$.

Step4: Use the APR table (conceptually)

The finance charge per $100$ of the amount financed is $\frac{102}{3102}\times100\approx 3.29$. For a 12 - month loan, looking up in the APR table (not shown here but in general practice), we find the APR. Since the finance charge per $100$ of the amount financed is approximately $3.29$, the APR is approximately 7.0%.

Answer:

a) $102 b) 7.0%