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Thread: maths in economics

  1. #1
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    maths in economics

    • Calculate the value of 1,200 invested for 5 years at 4% interest rate compounded:
      • annually
      • semi-annually
      • quarterly
      • continuously
      • How many years would it take for an amount of money invested at 4% interest rate compounded continuously to triple in value?
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  2. #2
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    Quote Originally Posted by daisy View Post
    • Calculate the value of 1,200 invested for 5 years at 4% interest rate compounded:
      • annually
      • semi-annually
      • quarterly
      • continuously
      • How many years would it take for an amount of money invested at 4% interest rate compounded continuously to triple in value?
    For the annual and quarterly compounding, go here:

    Balance Roll with Interest

    For start date and end date, just enter 2 dates with a 5 year difference, like 1/1/2008 and 1/1/2013.

    You should be able to figure out the semi-annually from here.
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  3. #3
    Super Member Aryth's Avatar
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    The compound Interest Equation is as follows:

    $\displaystyle P = C(1 + \frac{r}{n})^{nt}$

    where:

    $\displaystyle P = \text{Future Value}$

    $\displaystyle C = \text{Initial Deposit}$

    $\displaystyle r = \text{Interest Rate}$

    $\displaystyle n = \text{Number of times invested per year}$

    $\displaystyle t = \text{Number of years invested}$

    Let's go ahead and put what we know:

    $\displaystyle P = ?$

    $\displaystyle C = 1200$

    $\displaystyle r = .04$

    $\displaystyle n = \text{Varies}$

    $\displaystyle t = 5$

    1) Annually (n=1):

    $\displaystyle P = 1200(1 + .04)^{5}$

    $\displaystyle P = 1459.98$

    2) Semi-annually (n=2):

    $\displaystyle P = 1200(1 + \frac{.04}{2})^{10}$

    $\displaystyle P = 1462.79$

    3) Quarterly (n=4):

    $\displaystyle P = 1200(1 + \frac{.04}{4})^{20}$

    $\displaystyle P = 1464.23$

    4) Continuously ($\displaystyle n\to \infty$):

    This has a special equation:

    $\displaystyle P = Ce^{rt}$

    All the variables remain the same.

    $\displaystyle P = 1200e^{5(.04)}$

    $\displaystyle P = 1465.68$

    And there you go.
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  4. #4
    Member jonah's Avatar
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    How many years would it take for an amount of money invested at 4% interest rate compounded continuously to triple in value?
    $\displaystyle
    \begin{gathered}
    P = Ce^{rt} \hfill \\
    \Leftrightarrow \hfill \\
    t = \tfrac{1}
    {r} \cdot \ln \tfrac{P}
    {C} = \tfrac{1}
    {{.04}} \cdot \ln \tfrac{3}
    {1} \approx 27.46530721 \hfill \\
    \end{gathered}

    $

    or 27 years and 169.84 days
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