You want to purchase an automobile for $32,383. The dealer offers you​ 0% financing for 48 months or a $6,122 rebate. You can obtain 5.7% financing for 48 months at the local bank.

Question

You want to purchase an automobile for $32,383. The dealer offers you​ 0% financing for 48 months or a $6,122 rebate. You can obtain 5.7% financing for 48 months at the local bank.

1. Which option should you​ choose?

a. rebate - correct answer

b. 0% financing

1. How much money will you save per​ month?

​$ _________ ​(Round to two decimal​ places.)

Answer 1

To determine which option is more beneficial, let's compare the total cost of financing for both scenarios.

Option 1: 0% Financing with Rebate

Price of the automobile: $29,170

Rebate: $4,583

The financed amount will be reduced by the rebate:

Financed amount = $29,170 - $4,583 = $24,587

Since the financing is at 0%, there will be no interest charges.

Option 2: 6.3% Financing

Price of the automobile: $29,170

Interest rate: 6.3%

Number of months: 72

To calculate the monthly payment on a loan with these parameters, we can use the loan amortization formula:

Monthly payment = (P * r * (1 + r)^n) / ((1 + r)^n - 1)

Where:

P = Principal amount (loan amount)

r = Monthly interest rate (annual interest rate / 12)

n = Total number of payments (number of months)

Let's calculate the monthly payment for Option 2:

P = $29,170

r = 6.3% / 12 = 0.00525 (monthly interest rate)

n = 72

Monthly payment = ($29,170 * 0.00525 * (1 + 0.00525)^72) / ((1 + 0.00525)^72 - 1)

Monthly payment = $474.20

Now, let's compare the total cost of financing for both options over 72 months:

Option 1: 0% Financing with Rebate

Total cost = Monthly payment * Number of months

Total cost = $0 * 72 = $0

Option 2: 6.3% Financing

Total cost = Monthly payment * Number of months

Total cost = $474.20 * 72 = $34,150.40

To calculate the monthly savings, we subtract the total cost of Option 1 from the total cost of Option 2 and divide it by the number of months:

Monthly savings = (Total cost of Option 2 - Total cost of Option 1) / Number of months

Monthly savings = ($34,150.40 - $0) / 72 = $474.20

Therefore, if you choose the 0% financing with a rebate option, you will save $474.20 per month.

Answer 2

32383*1.00 4yr

32383-6122=26261

5.7% will cost you 32.780.17.

Formula: fv=p(1+int/c)^(nt)

26261(1+.057/1)^4=$32780.17 (bank)

future value

principal

int

times/yr

yrs

times/yr

Save 32780.17-32383=$397.17 if you pay full price from your pocket.