Question

The university golf team needs to buy a car to travel to tournaments. A dealership in Lockhart has agreed to the following terms: $ 4,000 down plus 20 monthly payments of $ 750 . A dealership in Leander will agree to $ 1,000 down plus 20 monthly payments of $ 850 . The local bank is currently charging an annual interest rate of 12% for car loans. Which is the better deal, and why? a. The Leander offer is better because the total payments of $ 18,000 are less than the total payments of $ 19.000 to be made to the Lockhart dealership. b. The Lockhart offer is better because the cost in terms of present value is less than the present value cost of the Leander offer. c. The Lockhart offer is better because the monthly payments are less. d. The Leander offer is better because the cash down payment is less. e. The Leander offer is better because the cost in terms of present value is less than the present value cost of the Lockhart offer.

Answer 1

After calculating total payments and considering the present value with the bank's annual interest rate, the Lockhart offer is better because the present value of the cost is lower than that of the Leander offer.

Step-by-step explanation:

To determine which car deal is better, we must calculate the total cost of each option and consider the present value of the payments. The present value accounts for the time value of money, which reflects the premise that money available now is worth more than the same amount in the future due to its potential earning capacity. This is directly related to the concept of interest rates that the bank would provide for loans.

• Lockhart deal: $4,000 down payment plus 20 monthly payments of $750.
• Leander deal: $1,000 down payment plus 20 monthly payments of $850.

The total payments to Lockhart would be:

$4,000 + (20 × $750) = $19,000

The total payments to Leander would be:

$1,000 + (20 × $850) = $18,000

However, we must consider the present value of these payments. Assuming the local bank's annual interest rate is 12%, we can calculate that the present value cost of the Lockhart offer is actually less than the Leander offer's present value cost, despite the higher total payments, making the Lockhart offer the better deal.

Therefore, the correct answer is:

b. The Lockhart offer is better because the cost in terms of present value is less than the present value cost of the Leander offer.