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Math Help - finding value of car

  1. #1
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    finding value of car

    hello,

    the value of a certain type of car depreicates 20% the first year and 5% each year afterwards. how would i find the value of 5 year old car of this tyoe which originally sold for $4000

    can someone please demontrate how a question of this form is solved?
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  2. #2
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    Quote Originally Posted by sigma1 View Post
    hello,

    the value of a certain type of car depreicates 20% the first year and 5% each year afterwards. how would i find the value of 5 year old car of this tyoe which originally sold for $4000

    can someone please demontrate how a question of this form is solved?
    Let P_0 be the original price

    After one year the car loses 20% of P: P_1 = 0.8P_0 = (1-0.2)P_0

    Thereafter the car loses 5% each year (let t be the time in years): P_t = P_1(1-0.05)^{t-1}

    If we combine these expressions together we get the form P_t = P_0(1-0.2)(1-0.05)^{t-1} = 0.8P_0 \cdot 0.95^{t-1}



    Since you know P_0 and t you can substitute in order to find P_5
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  3. #3
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    thanks alot, i would have tried to solve that from first principles..
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