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6 March, 05:20

The price of a car that you want is $70,000 today. its price is expected to increase by $3300 per year. you now have $35,000 in an investment which is earning 15% per year. the number of years before you have enough to buy the car without borrowing any money is closest to:

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  1. 6 March, 05:46
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    Let n=number of years

    Price of car

    = 70000 * (3300n)

    Value of investment

    = 35000 * (1+0.15) ^n

    To afford to buy the car,

    Value of investment > = Price of car, or

    35000 (1.15) ^n >=70000*3300n

    =>

    35000 (1.15) ^n / 70000 >=3300n

    =>

    1.15^n >=6600n,

    solve using Newton's approximation.

    f (n) = 1.15^n-6600n = 0

    f' (n) = 0.13976 (1.15^n) - 6600

    try n0=100

    n1=n0-f (n0) / f' (n0)

    =100-f (100) / f' (100)

    =96.74

    n2=n1-f (n1) / f' (n1)

    =95.65

    n3=n2-f (n2) / f' (n2)

    =95.55

    So the answer is it takes 96 years to have enough money to buy the car without borrowing.
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