Question

Joslyn has decided to purchase a $19,500 car and would like to finance it for five years. Her bank has offered her a standard 7.9% APR, while the dealership has offered her a special 5.9% APR. How much money will she save each month by choosing financing through the dealership? A. $14.61 B. $29.45 C. $18.38 D. $16.25

Answer 1

To determine the monthly savings by choosing the dealership's 5.9% APR over the bank's 7.9% APR for a $19,500 car financed over five years, apply the installment loan formula to each APR and then calculate the difference between the two resulting monthly payments.

Step-by-step explanation:

Joslyn is considering financing options for a $19,500 car over a five-year period and wants to know how much money she will save each month by choosing financing through the dealership at a 5.9% APR instead of her bank's 7.9% APR.

To calculate the monthly payment for each APR, we can use the formula for an installment loan, which is:

M = P [ i(1 + i)^n ] / [ (1 + i)^n - 1]

where:

• M is the monthly payment
• P is the principal amount ($19,500)
• i is the monthly interest rate (annual rate / 12)
• n is the number of payments (5 years x 12 months/year)

For the bank's 7.9% APR:

i = 7.9% / 12 = 0.007583

n = 5 x 12 = 60

For the dealership's 5.9% APR:

i = 5.9% / 12 = 0.004916

Calculating separately each monthly payment and then finding the difference will give us the amount saved per month by choosing the dealership's offer over the bank's.