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**

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