Question

After deciding to get a new car, you can either lease the car or purchase it with a two-year loan. The car you wish to buy costs $34,500. The dealer has a special leasing arrangement where you pay $98 today and $498 per month for the next two years. If you purchase the car, you will pay it off in monthly payments over the next two years at an APR of 5 percent, compounded monthly. You believe that you will be able to sell the car for $22,500 in two years.
   
What is the cost today of purchasing the car? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)
  
Cost of purchasing           $ 3450 3450 Incorrect
  
What is the cost today of leasing the car? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)
  
Cost of leasing           $ 12050 12050 Incorrect

What break-even resale price in two years would make you indifferent between buying and leasing? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)
  
Break-even resale price           $ 1.45 1.45 Incorrect

Answer 1

Solution:

When you purchase the car, you will make regularly scheduled installments and at you tend 2 years, you will get $22,500 at a bargain.

The cost today of purchasing the car :

= $34,500 – $22,500/(1 + 0.05/12)^24

The cost today of purchasing the car = $10,860.31

The cost today of leasing the car :

= $98 + ($498/(0.05/12)) * (1 – 1/(1 + 0.05/12)^24)

The cost today of leasing the car = $11,449.36

To make indifferent between the options, the PV of both costs must be same and required resale price be S. $34,500 – S/(1 + 0.05/12)^24 = $11,449.36

S/(1 + 0.05/12)^24 = $34,500 - $11,449.36

S/(1 + 0.05/12)^24 =$23,050.64

S = $23,050.64 * (1 + 0.05/12)^24

= $25,469.60

Break-even resale price = $25,469.60