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Math Help - Macroeconomics Math Problem Help, Please?

  1. #1
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    Macroeconomics Math Problem Help, Please?

    Consider a hypothetical economy that grows at a rate of 4% per year. Approximately how many years will it take for this economy to double in size?
    Note: the size of an economy is its real GDP.
    Hint: to solve this problem, you first want to set up an equation that links the future size of the economy to its current size and the growth rate.



    Honestly I have no idea where to start. If anyone has any clue as to solve this I would greatly appreciate some help!
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  2. #2
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    Re: Macroeconomics Math Problem Help, Please?

    Quote Originally Posted by michellederz View Post
    Consider a hypothetical economy that grows at a rate of 4% per year. Approximately how many years will it take for this economy to double in size?
    Note: the size of an economy is its real GDP.
    Hint: to solve this problem, you first want to set up an equation that links the future size of the economy to its current size and the growth rate.



    Honestly I have no idea where to start. If anyone has any clue as to solve this I would greatly appreciate some help!
    think of the economy as a bank account with some interest rate.

    It's future value FV (FV) is given, in terms of the interest rate (R), time (T), and present value (PV) as

    $$FV=PV(1+R)^T$$

    In this problem you are looking for the time T it takes for FV/PV=2, i.e. the economy has doubled.

    $$2=(1+0.04)^T$$

    $$\log(2)=T\log(1.04)$$

    $$T=\frac{\log(2)}{\log(1.04)}$$

    $$T \approx 17.67\text{yrs}$$
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  3. #3
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    Re: Macroeconomics Math Problem Help, Please?

    Quote Originally Posted by romsek View Post
    think of the economy as a bank account with some interest rate.

    It's future value FV (FV) is given, in terms of the interest rate (R), time (T), and present value (PV) as

    $$FV=PV(1+R)^T$$

    In this problem you are looking for the time T it takes for FV/PV=2, i.e. the economy has doubled.

    $$2=(1+0.04)^T$$

    $$\log(2)=T\log(1.04)$$

    $$T=\frac{\log(2)}{\log(1.04)}$$

    $$T \approx 17.67\text{yrs}$$
    Ahhh! That makes so much more sense thinking of it in those terms. Thank you so much.
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