Let's solve Rudy's problem step-by-step.
1. Determine the amount to be financed:
- Car price: [tex]\( \$10,240 \)[/tex]
- Trade-in allowance: [tex]\( \$3,000 \)[/tex]
- Down payment: [tex]\( \$2,000 \)[/tex]
The amount to be financed is:
[tex]\[
10240 - 3000 - 2000 = 5240 \, \text{dollars}
\][/tex]
2. Find the monthly car loan payment:
According to the table provided, the monthly car loan payment per [tex]$1000 borrowed at 3.4% APR for a 36-month term is 29.258 dollars.
Since Rudy is borrowing \(\$[/tex]5240\), we calculate his monthly payment as follows:
[tex]\[
\left( \frac{5240}{1000} \right) \times 29.258 = 5.24 \times 29.258 = 153.31192 \, \text{dollars per month}
\][/tex]
3. Calculate the total payment over the 36 months:
The total payment over the life of the loan is the monthly payment multiplied by the number of months:
[tex]\[
153.31192 \times 36 = 5519.22912 \, \text{dollars}
\][/tex]
4. Find the total interest paid:
The total interest paid is the difference between the total payment and the amount financed:
[tex]\[
5519.22912 - 5240 = 279.22912 \, \text{dollars}
\][/tex]
5. Round the total interest to the nearest dollar:
[tex]\[
\text{Rounded total interest} = 279 \, \text{dollars}
\][/tex]
Therefore, the total amount of interest Rudy will pay over the 3-year period, rounded to the nearest dollar, is [tex]\(\boxed{279}\)[/tex] dollars.
