Let's break down the problem into the steps required to find the amount financed, total finance charge, and the APR based on the given data.
### Given Data:
- Purchase price of a used car: [tex]$5,633
- Down payment: $[/tex]1,203
- Number of monthly payments: 48
- Total of monthly payments: [tex]$5,689.76
### Step-by-Step Solution:
#### (a) Amount Financed:
The amount financed is calculated by subtracting the down payment from the purchase price.
\[
\text{Amount Financed} = \text{Purchase Price} - \text{Down Payment}
\]
Substituting in the values:
\[
\text{Amount Financed} = 5633 - 1203 = 4430
\]
So, the amount financed is $[/tex]4,430.
#### (b) Total Finance Charge:
The total finance charge is computed by subtracting the amount financed from the total of monthly payments.
[tex]\[
\text{Total Finance Charge} = \text{Total of Monthly Payments} - \text{Amount Financed}
\][/tex]
Substituting in the values:
[tex]\[
\text{Total Finance Charge} = 5689.76 - 4430 = 1259.70
\][/tex]
So, the total finance charge is [tex]$1,259.70.
#### (c) APR by Table Lookup:
To determine the APR, one typically looks up the value in a table, such as Table 141, based on the given values and terms. However, the exact table lookup details are not provided in this problem, and the result shows the APR as `None`.
### Summary:
- Amount Financed: $[/tex]4,430
- Total Finance Charge: [tex]$1,259.70
- APR: To be determined by specific table lookup (as indicated by `None` in the result).
So, the solution for the problem is:
1. Amount Financed: $[/tex]4,430
2. Total Finance Charge: $1,259.70
3. APR: Not specified (requires table lookup).
These steps outline the process for calculating the necessary values based on the given data.
