Select the correct answer.

Bob has taken out a loan of \[tex]$15,000 for a term of 48 months (4 years) at an interest rate of 6.5%. Using the amortization table provided, what will be his total finance charge over the course of his loan?

\begin{tabular}{|l|l|l|l|l|l|}
\hline
\multicolumn{5}{|c|}{ Monthly Payment per \$[/tex]1,000 of Principal } \\
\hline
Rate & 1 Year & 2 Years & 3 Years & 4 Years & 5 Years \\
\hline
6.5\% & \[tex]$86.30 & \$[/tex]44.55 & \[tex]$30.65 & \$[/tex]23.71 & \[tex]$19.57 \\
\hline
7.0\% & \$[/tex]86.53 & \[tex]$44.77 & \$[/tex]30.88 & \[tex]$23.95 & \$[/tex]19.80 \\
\hline
7.5\% & \[tex]$86.76 & \$[/tex]45.00 & \[tex]$31.11 & \$[/tex]24.18 & \[tex]$20.04 \\
\hline
8.0\% & \$[/tex]86.99 & \[tex]$45.23 & \$[/tex]31.34 & \[tex]$24.41 & \$[/tex]20.28 \\
\hline
8.5\% & \[tex]$87.22 & \$[/tex]45.46 & \[tex]$31.57 & \$[/tex]24.65 & \[tex]$20.52 \\
\hline
9.0\% & \$[/tex]87.45 & \[tex]$45.68 & \$[/tex]31.80 & \[tex]$24.89 & \$[/tex]20.76 \\
\hline
\end{tabular}

A. \[tex]$355.65
B. \$[/tex]975.00
C. \[tex]$1,682.40
D. \$[/tex]2,071.20
E. \$17,071.20



Answer :

To determine Bob's total finance charge over the course of his loan, we follow these steps:

1. Identify the monthly payment per [tex]$1,000 of principal for a 4-year term at 6.5% interest rate: From the table, the monthly payment per $[/tex]1,000 for a 4-year term at 6.5% interest is [tex]$23.71. 2. Calculate the monthly payment for Bob's loan: Bob's loan amount is $[/tex]15,000. To find the monthly payment, multiply the loan amount in thousands by the monthly payment rate:
[tex]\[ \text{Monthly Payment} = \left(\frac{15,000}{1,000}\right) \times 23.71 = 15 \times 23.71 = \$355.65 \][/tex]

3. Calculate the total amount paid over the course of the loan:
Since the loan term is 4 years, which is 48 months, multiply the monthly payment by the number of months to get the total amount paid:
[tex]\[ \text{Total Amount Paid} = 355.65 \times 48 = \$17,071.20 \][/tex]

4. Determine the total finance charge:
The finance charge is the difference between the total amount paid and the principal loan amount. Subtract the original loan amount from the total amount paid:
[tex]\[ \text{Finance Charge} = 17,071.20 - 15,000 = \$2,071.20 \][/tex]

Therefore, Bob's total finance charge over the course of his loan is:
[tex]\[ \boxed{\$2,071.20} \][/tex]

So, the correct answer is:
D. \$2,071.20