A car dealer carries out the following calculations. What is the annual percentage rate? (Round your answer to the nearest tenth.)
List price $5,368.00
Options $1,625.00
Destination charges $200.00
Subtotal $7,193.00
Tax $431.58
Less trade-in $2,932.00
Amount to be financed $4,692.58
8% interest for 48 months $1,501.63
MONTHLY PAYMENT $129.05
_____%
To calculate the annual percentage rate (APR), we need to know the total amount of interest paid over the loan term.
The total interest paid can be calculated by subtracting the amount to be financed from the sum of the monthly payment amounts over the loan term:
Total Interest = (Monthly Payment * Loan Term) - Amount to be financed
In this case, the total interest paid would be:
Total Interest = (129.05 * 48) - 4692.58
Total Interest = 6194.40 - 4692.58
Total Interest = 1501.82
Now, to calculate the APR, we divide the total interest paid by the amount to be financed, and then multiply by 100 to get the percentage:
APR = (Total Interest / Amount to be financed) * 100
APR = (1501.82 / 4692.58) * 100
APR ≈ 32.0%
Therefore, the annual percentage rate (APR) for this car loan is approximately 32.0%.
To find the annual percentage rate (APR), we need to use the given information about the loan. The APR represents the annual cost of borrowing, including both the interest rate and any additional fees or charges associated with the loan.
In this scenario, we are given the monthly payment amount ($129.05), the loan amount ($4,692.58), and the loan term (48 months).
To calculate the APR, we can use the following formula:
APR = (Total Interest / Loan Amount) * (12 / Loan Term) * 100
1. First, let's calculate the total interest paid over the course of the loan. Since we know the monthly payment amount, the loan term, and the loan amount, we can subtract the loan amount from the sum of all monthly payments to find the total interest paid:
Total Interest = (Monthly Payment * Loan Term) - Loan Amount
Total Interest = ($129.05 * 48) - $4,692.58
Total Interest = $6,202.40 - $4,692.58
Total Interest = $1,509.82
2. Now that we have the total interest, we can calculate the APR using the formula mentioned earlier:
APR = (Total Interest / Loan Amount) * (12 / Loan Term) * 100
APR = ($1,509.82 / $4,692.58) * (12 / 48) * 100
APR = 0.3214 * 0.25 * 100
APR = 0.0804 * 100
APR = 8.04%
Therefore, the annual percentage rate (APR) for this car loan is approximately 8.04%.