Question

# After deciding to get a new car, you can either lease the car or purchase it...

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

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

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