Short Answer 
The final answer for the extra interest paid on a car loan when comparing a 15% interest rate to a 6% interest rate is **$14,814.00**. This result is derived from calculating the total payments for each interest rate and finding the difference between them.
Step 1: Understanding the Loan Variables
When dealing with the loan for a car, we need to clearly define our variables:
- p = Principal amount, which is $45,000.
- r = Monthly interest rate; if the annual rate is 15%, divide by 12 for r = 0.0125, and if it is 6%, r = 0.0005.
- n = Total number of monthly payments, calculated as the loan term in years multiplied by 12, so for 6 years, n = 72.
Step 2: Calculating Monthly Payments
Using the amortization formula, we can find the monthly payments for both interest rates:
- For 15% interest: Use the formula to calculate the monthly payment, yielding approximately $951.53.
- For 6% interest: The calculation gives a monthly payment of about $745.78.
Step 3: Determining Total Payments and Extra Interest
To find the total cost of the loan and the extra interest, we perform the following calculations:
- For the 15% loan: Total cost = $951.53 √ó 12 √ó 6 = $68,510.16.
- For the 6% loan: Total cost = $745.78 √ó 12 √ó 6 = $53,696.16.
- Finally, subtract the latter from the former to find the extra interest: $68,510.16 – $53,696.16 = $14,814.00.