Sure, let's solve this problem step-by-step explaining how each element is found:
### 1. Determine the Monthly Payment
The amount borrowed is [tex]$15,000 and the term of the loan is 4 years. The table provided shows that for a 4-year loan at an interest rate of 6.5%, the monthly payment per $[/tex]1,000 of the principal is \[tex]$23.71.
Calculation:
To find the monthly payment, we first calculate how much Bob pays per month for the entire loan amount.
\[
\text{Monthly Payment} = \left(\frac{\$[/tex]15,000}{\[tex]$1,000}\right) \times \$[/tex]23.71 = 15 \times \[tex]$23.71 = \$[/tex]355.65
\]
### 2. Determine the Total Payment over the Term of the Loan
Bob will make this monthly payment over 4 years, which amounts to:
[tex]\[
4 \, \text{years} \times 12 \, \text{months/year} = 48 \, \text{months}
\][/tex]
Calculation:
The total amount Bob will have paid by the end of the loan term is:
[tex]\[
\text{Total Payment} = \text{Monthly Payment} \times \text{Total Number of Payments} = \$355.65 \times 48 = \$17,071.20
\][/tex]
### 3. Calculate the Total Finance Charge
The finance charge is the total amount paid minus the amount borrowed. Thus, it represents the cost of borrowing the money.
Calculation:
[tex]\[
\text{Total Finance Charge} = \text{Total Payment} - \text{Loan Amount} = \$17,071.20 - \$15,000 = \$2,071.20
\][/tex]
### Conclusion
After completing all the above calculations, the total finance charge over the course of Bob's loan is \[tex]$2,071.20.
Therefore, the correct answer is:
D. \$[/tex]2,071.20
