Question

Kangaroo Autos is offering free credit on a new $10,000 car: You pay $1,000 down and then $300 a month for the next 30 months. Turtle Motors next door does not offer free credit but will give you $1,000 off the list price.
If the interest rate is 12% a year, which dealership is offering you the better deal?

Answer 1

Answer:

Kangaroo Auto offers the better deal

If the I go for Kangaroo Autos, then I will save $257.69 in today's term

Explanation:

Here we need to compare the present value of the two options;

Present value is the worth today of an amount or series of amount payable or receivable in the future period.

Where a series of equal amount is receivable or payable in the future it is called an annuity.

One of the payment options includes an annuity. Therefore, we need to work out the present value of the annuity. This is done using the following formula:

Present Value = A ×( 1 - (1+r)^(-n))/r

where A = equal cash flow, r- rate per period, n - no. of periods

A = 300, r- rate per month - 12%/12 = 1% , n= 30

PV = 300 ×(1- (1+0.01)^(-30))/0.01

    = 300 × 25.877

     =7,742.31

Now we can work out he cost of each option  and comapare them in today's Dollar:

Option 1 : Kangaroo Autos

Total cost of option 1 = deposit + PV of annuity

                                  =   1000 + 7,742.31

              cost              = 8,742.31

Option 2: Turtle Motors:

Price =  Car price - Discount

        =   $10,000 - $1000

     cost    =   $9,000

Kangaroo Auto offers a better  deal.

If  I go for Kangaroo Autos, then I will save $257.69 in today's term