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Math Help - Accounting problem

  1. #1
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    Accounting problem

    Assets such as houses, cars, business equipment, and art appreciate or depreciate with time. The formula used to compute compound interest can be used to find the future value of these assets. Depreciation or appreciation is given in terms of one year, so n = 1 in the formula A = P(1 + r/n)^nt. This makes the formula for the future value of an object A = P(1 + r)^t, where P is the initial value, r is the rate of appreciation or depreciation, and t is the time in years. If the object is appreciating, then r > 0. If the object is depreciating, then r < 0.

    a) You are considering buying a new car that has a list price of $12000. A book that gives comparisons of different cars says that in the past years this model has depreciated at a rate of 15% per year. If you are planning on keeping the car for five years, how much would you expect the car to be worth when you are ready to sell it?

    b) Homes in a particular area appreciate at a rate of about 4% per year. If a home sold for $89000 this year, after how many year would you expect the home to be worth $124000?

    c) Inflation causes prices to rise over time. The rate of inflation in each country fluctuates in reaction to various economic conditions. Suppose the rate of inflation in the United States averaged 3.5%. If a school lunch costs $1.85 today and a friend says he paid $1.35 for the same type of lunch some time ago, how long ago do you think he bought his lunch?

    This is was the final problem on the lesson on exponential and logarithmic equations in my book. I'm drawing a blank on how to solve these kind of problems though.
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  2. #2
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    Re: Accounting problem

    Quote Originally Posted by explodingtoenails View Post
    Assets such as houses, cars, business equipment, and art appreciate or depreciate with time. The formula used to compute compound interest can be used to find the future value of these assets. Depreciation or appreciation is given in terms of one year, so n = 1 in the formula A = P(1 + r/n)^nt. This makes the formula for the future value of an object A = P(1 + r)^t, where P is the initial value, r is the rate of appreciation or depreciation, and t is the time in years. If the object is appreciating, then r > 0. If the object is depreciating, then r < 0.

    a) You are considering buying a new car that has a list price of $12000. A book that gives comparisons of different cars says that in the past years this model has depreciated at a rate of 15% per year. If you are planning on keeping the car for five years, how much would you expect the car to be worth when you are ready to sell it?

    A = 12000(0.85)^5

    b) Homes in a particular area appreciate at a rate of about 4% per year. If a home sold for $89000 this year, after how many year would you expect the home to be worth $124000?

    124000 = 89000(1.04)^t
    solve for t


    c) Inflation causes prices to rise over time. The rate of inflation in each country fluctuates in reaction to various economic conditions. Suppose the rate of inflation in the United States averaged 3.5%. If a school lunch costs $1.85 today and a friend says he paid $1.35 for the same type of lunch some time ago, how long ago do you think he bought his lunch?

    you try this one yourself
    ...
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  3. #3
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    Re: Accounting problem

    For c would it be:

    1.85 = 1.35(.035)^t

    and then I solve for t?
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  4. #4
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    Re: Accounting problem

    1.85 = 1.35(.035)^t

    Not quite: 1.85 = 1.35(1 + .035)^t

    Solve fot t.
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