Question

You have decided to acquire a new car that costs $30,000. You are considering whether to lease it for three years or to purchase it and financing the purchase with a three year installment loan. The lease requires no down payment and lasts for three years. Lease payments are $400 monthly starting immediately, whereas the installment loan will require monthly payments starting a month from now at an annual percentage rate (APR) of 8%. The discount rate (APR) is also 8%. 1) If you expect the resale value of the car to be $20,000 three years from now, should you buy or lease it? 2) What is the break-even resale price of the care three years from now, such that you would be indifferent between buying and leasing it?

Answer 1

Leasing the car would be more advantageous as the total cost of leasing is lower than the total cost of buying. The break-even resale price of the car three years from now would be $17,779.36.

Step-by-step explanation:

To determine whether to buy or lease the car, we need to compare the total costs of each option. For leasing, the total cost is the sum of the monthly lease payments. In this case, it would be $400/month for 36 months, which amounts to $14,400. For buying, we need to consider the purchase price of $30,000, minus the expected resale value of $20,000 after three years, resulting in a net cost of $10,000. Additionally, we need to factor in the interest on the loan. With an APR of 8%, the monthly payment for the loan would be approximately $618.28. Over three years, the total cost of the loan would be $22,179.36. Adding the net cost of $10,000, the total cost of buying would be $32,179.36. Since the total cost of leasing is lower than the total cost of buying, it would be more advantageous to lease the car.

To calculate the break-even resale price, we set the total cost of leasing equal to the total cost of buying. Using the same calculations as before, we can rearrange the equation and solve for the resale price:

(Lease cost) = (Purchase cost) - (Resale price) + (Loan cost)

Substituting in the given values:

$14,400 = $10,000 - (Resale price) + $22,179.36

Simplifying the equation:

(Resale price) = $10,000 + $22,179.36 - $14,400

(Resale price) = $17,779.36

Therefore, the break-even resale price of the car three years from now would be $17,779.36.

Answer 2

The Answer Is 1 Because You Have To Resale The Valie Of The Car