Short Answer 
To calculate the total cost of a car loan, identify the principal, interest rates (15% and 6%), and payment periods (72 months). Monthly payments are $951.53 at 15% and $745.78 at 6%, leading to total payments of $68,510.16 and $53,696.16 respectively, resulting in a $14,814.00 difference in costs due to the higher interest rate.
Step 1: Understand the Loan and Interest Calculation
To determine the total cost of a car loan, it is essential to grasp the essential components of loan calculations. You will need to identify the principal, the monthly interest rate, and the number of payment periods involved. In this case, the principal is valued at $45,000, with two different interest rates considered: 15% and 6%. The total number of payments is calculated as 72 (6 years x 12 months).
Step 2: Calculate Monthly Payments for Different Interest Rates
Using the formula for monthly payment calculations, plug in the values for each interest rate. The formula for monthly payments is:
- For 15% interest:
- Monthly payment = $951.53
- For 6% interest:
- Monthly payment = $745.78
This information will allow you to compute the total costs paid over the loan period for both interest rates.
Step 3: Determine the Difference in Total Payment Costs
Finally, calculate the total payment for both interest rates to find the difference in costs. The calculations are:
- Total cost at 15%: $951.53 x 12 x 6 = $68,510.16
- Total cost at 6%: $745.78 x 12 x 6 = $53,696.16
- Difference: $68,510.16 – $53,696.16 = $14,814.00
This final amount, $14,814.00, represents the extra interest paid due to the higher interest rate, effectively concluding the problem.