After deciding to buy a new car, you can either lease the car or purchase it on

Question

After deciding to buy a new car, you can either lease the car or purchase it on a three-year loan. The car you wish to buy costs $39,500. The dealer has a special leasing arrangement where you pay $108 today and $508 per month for the next three years. If you purchase the car, you will pay it off in monthly payments over the next three years at a 6 percent APR. You believe you will be able to sell the car for $27,500 in three years.

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

What is the present value of purchasing the car? (Do not round intermediate calculations and round your final answer to 2 decimal places. (e.g., 32.16))

Explanation / Answer

First we will calculate how much money is paid if we go for lease

Down payment is $108

For next 36 months we pay $508 per month

The total amount paid is

= 508 * 36 + 108

= 18288 + 108

= $ 18396

Now we go for buying the car the total amount paid for 3 years is going to use the formula for interest compounded monthly to find the amount of your total payment of $39,500 for three years with 6% interest if you buy it.

P = A(1 + r/n)^(nt)

A = 39,500
r = 0.06
t = 3
n = 12

P = $47268.88

Then if you sell it for $27,500 your total cost is

47268.88 - 27500 = 19768.88
************************

Difference between buy and lease is:
19768.88 - 18396 = 1372.88

If you want to break even, your resale price needs to have $1372.88 higher

to calculate present value of car , we will use the following formula

PV loan = (Price of the Car – PV of the Resale Price)

The present value factor of $1 received at end of 36 months at 0.5% interest rate is 0.8356

The present value of resale of car is 27,500 * 0.8356 = $22,979

Present value of car is $39,500 - $22,979 = $16,521

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