# Which option should you choose? Why?You want to purchase an automobile for \$28,500.The dealer offers you 0% financing for 60 months or a \$ 6,000 rebate. You can obtain 6.2% financing for 60 months...

Which option should you choose? Why?

You want to purchase an automobile for \$28,500.The dealer offers you 0% financing for 60 months or a \$ 6,000 rebate. You can obtain 6.2% financing for 60 months at the local bank. Which option should you choose? Explain clearly your options for this decision. What is your decision? Why?

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Option (1)

If you have 0% financing for 60 months, then you pay a total of \$28,500, which is the complete price of the car.

Option (2)

In this case, you need to finance the car through your bank but you get a rebate from the car company.  This means the amount you need to finance is \$28500-\$6,000=\$22,500.  The bank has an interest rate of 6.2% financing for 60 months.  It appears that the interest rate is per year and since the question does not say, we shall pay the entire loan back at the end of the 60 months and the interest is compounded yearly.  This means that the amount owed at the end of the 5 year period is

`A=A_0(1+r)^t`   where `A_0` is the amount of the loan, `t` is the time (5 years) and `r` is the interest rate (0.062).

The amount owed at the end of the loan is

`A=22500(1.062)^5=\$30,395.21`

Since the amount owed with option 1 is less than with option 2, you should have the 0% financing from the dealer.