A car dealer will sell you a used car for $8,672 with $672 down and payments of $157.66 per month for 60 months. What is the APR? (Use the formula on page 156. Round each answer to the nearest tenth.)
To find the APR (Annual Percentage Rate) of the car loan, we can use the formula on page 156. The formula is:
APR = (2 * N * C) / (P * (N + 1))
Where:
APR is the Annual Percentage Rate
N is the total number of payments
C is the finance charge (total cost of the loan)
P is the principal (loan amount)
In this case, the principal is $8,672, the down payment is $672, and the monthly payment is $157.66. We need to calculate the finance charge as the difference between the total cost of the loan and the principal.
Total cost of the loan = (Monthly payment * Number of payments) - Down payment
Total cost of the loan = ($157.66 * 60) - $672
Total cost of the loan = $9,459.60 - $672
Total cost of the loan = $8,787.60
Now we can substitute the values into the formula:
APR = (2 * 60 * $8,787.60) / ($8,672 * (60 + 1))
First, calculate the numerator:
Numerator = 2 * 60 * $8,787.60
Numerator = $1,052,512
Then, calculate the denominator:
Denominator = $8,672 * (60 + 1)
Denominator = $8,672 * 61
Denominator = $529,952
Finally, calculate the APR:
APR = Numerator / Denominator
APR = $1,052,512 / $529,952
APR ≈ 1.986
The APR is approximately 1.986 or 1.99% when rounded to the nearest tenth.