Answer:
The Annual Percentage Rate, APR = 1.07%
Explanation:
The annual percentage rate (APR) for a loan is the amount payed annually as interest which is specified as a percentage of the balance of the loan
The given parameters are;
The cash price for the car the Colvilles are buying = $35,000.00
The amount of down payment they will make = 20% or $5,000
The will cover the balance by installment loan
The number of monthly with which the loan will be repaid, n = 48 monthly payment
The amount of the monthly payments, M = $651
The balance which will be taken on loan, P = 35,000.00 - 5,000 = 30,000
The balance which will be taken on loan, P = $30,000
[tex]APR = \left(\left(\dfrac{\dfrac{Fees + Interest}{Principal} }{n} \right) \times 12\right) \times 100[/tex]
[tex]APR = \left(\left(\dfrac{\dfrac{ I}{P} }{n} \right) \times 12\right) \times 100[/tex]
Therefore;
The interest paid over life of loan, I = M × n - P
∴ I = 651 × 48 - 30,000 = 1,284
Therefore, we have;
[tex]APR = \left(\left(\dfrac{\dfrac{ 1,284}{30,000} }{48} \right) \times 12\right) \times 100 = 1.07 \%[/tex]
The Annual Percentage Rate APR = 1.07%
