Question

You want to purchase an automobile for $ 26 comma 706. The dealer offers you​ 0% financing for 60 months or a $ 3 comma 926 rebate. You can obtain 6.3 % financing for 60 months at the local bank. Which option should you​ choose? Explain.

Answer 1

Answer:

Since the monthly payment with rebate is lower than monthly payment for 0% financing, I will choose the $3,926 rebate

Step-by-step explanation:

Price of the automobile = $26,706

There is 0% financing for 60 months

Rate = 6.3%

Monthly payment for 0% financing = 26706 ÷ 60 = $445.1

Rebate = $3,926

Monthly payment for $3926 rebate

Formula for calculating present value ( PV)  for Annuity payment

$P = \frac{r * PV}{1 - (1+r)^{-n} }$...................(1)

P = monthly payment

r = Rate per period = 6.3%/12

r =(6.3/100)/12 = 6.3/1200

r = 0.00525

Present value,  PV = 26706 - 3926 = $22780

number of payments, n = 60

Substituting these values into the equation (1) above

$P = \frac{0.00525 * 22780}{1 - (1+0.00525)^{-60} }$

P = $443.59

Note : From calculations, Monthly payment with rebate = $443.59, while monthly payment for 0% financing = $445.1

Since the monthly payment with rebate is lower than monthly payment for 0% financing, I will choose the $3,926 rebate