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30 December, 04:07

After deciding to acquire a new car, you can either lease the car or purchase it with a three-year loan. The car you want costs $38,000. The dealer has a leasing arrangement where you pay $105 today and $505 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 an APR of 6 percent. You believe that you will be able to sell the car for $26,000 in three years. a. What is the present value of leasing the car

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  1. 30 December, 04:15
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    The present value of leasing the car is $16,704.86 and the break even sale price is $25483.48.

    Explanation:

    Solution

    Given that

    The monthly rate = 0.06/12 = (6%/12)

    the number of period = 3 * 12 = 23

    Now

    The present value of leasing the car is computed below:

    Payment day = $105

    add: Present value of future monthly payment = 505 * (1 - (1 + (0.06/12)) ^-36 / (0.06/12)

    = 166,599,86

    Present value of the car = $105 + $166,599,86

    =$16,704.86

    Thus

    The present value of purchasing the car:

    Purchase cost = $38,000

    Less: present value of resale = 26000 / (1 + (0.06/12)) ^-36

    =21,726.77

    Present value of purchasing the car is $38,000 + $21,726.77

    =$16,273.23

    Now

    The break even sale price

    Let the resale price be x

    38000 - (x / ((1 + (0.06/12)) ^-36 = 16704.86

    (x / ((1 + (0.06/12)) ^-36 = 38000 - 16704.86

    (x / ((1 + (0.06/12)) ^-36 = 21295.14

    x = ((1 + (0.06/12)) ^-36 * 212954.14

    x = 25483.48

    Therefore the present value of leasing the car is $16,704.86 and the break even sale price is $25483.48
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