You are interested in a new Ford Taurus. After visiting your Ford dealer, doing your research on the best leases available, you have three options. (i) Purchase the car for cash and receive a $1,900 cash rebate from Dealer A. The price of the car is $19,000. (ii) Lease the car from Dealer B. Under this option, you pay the dealer $550 now and $225 a month for each of the next 36 months (the first $225 payment occurs 1 month from today). After 36 months you may buy the car for $10,900. (iii) Purchase the car from Dealer C who will lend you the entire purchase price of the car for a zero interest 36-month loan with monthly payments. The car price is $19,000. Suppose the market interest rate is 4%.

Okay: Dealer A's net cost is $19,000 minus the $1,900 rebate. Dealer B offers $225 times 36 months plus the $550 down payment, plus the $10,900 purchase price at the end of the lease.

Dealer C offers zero interest so the net cost is $19,000. You do the math.

So, what is the question?

What is the net cost today of the cheapest option?

To which option does the 4% interest rate go....all or the last two?

No, it does not apply to any of them.

Paying cash involves no loan or interest rate. There is no loan involved in a lease. The third dealer offers zero interest.

Ok thanks for your help

To determine the best option among the three choices, we need to calculate the present value of each option and compare them.

Let's start with option (i):

The price of the car is $19,000, and you receive a $1,900 cash rebate. Therefore, the net cost of the car is:
$19,000 - $1,900 = $17,100

Next, let's calculate the present value of option (ii) - leasing the car:

You pay $550 upfront and $225 per month for 36 months. The first $225 payment occurs 1 month from today. To calculate the present value, we need to discount each payment to its present value using the market interest rate of 4%. We can use the formula for the present value of an annuity:

Present Value of Annuity = Payment per period * [1 - (1 + r)^(-n)] / r

Where:
r = interest rate per period
n = number of periods

Using this formula:

Present Value of Monthly Payments = $225 * [1 - (1 + 0.04)^(-36)] / 0.04 = $6,490.07

After 36 months, there is an option to buy the car for $10,900. However, this amount is not relevant for present value calculations since it occurs in the future.

Lastly, let's calculate the present value of option (iii) - purchasing the car with a zero-interest loan:

Since the loan is interest-free, the present value of monthly payments will be the same as the loan amount itself.

Present Value of Loan = $19,000

Now, let's compare the present values of the three options:

(i) Net cost of purchasing the car for cash = $17,100
(ii) Present value of leasing the car = $6,490.07
(iii) Present value of purchasing with a zero-interest loan = $19,000

Based on the present values, the best option among the three is option (ii) - leasing the car from Dealer B, as it has the lowest present value of $6,490.07.