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Math Help - CAGR Question...

  1. #1
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    Exclamation CAGR Question...

    Hello!

    I need some help with a growth rate problem (bare with me, I'm bad with math...)

    Ok:

    I'm trying to figure out how to calculate something...

    In year 1, say I have $1916.4612
    In year 6, I have $2448.1061
    I have a calculated a CAGR of 4.16%
    ((1916.4612/2448.1061)^(1/6))-1

    So, if I want to estimate the amount for year 7... can I just take $2448.1061 x 4.16% to get $2550.0690? I'm not sure if that's right...

    Please help!
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  2. #2
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    Hi there

    You should consider the following model

    A = P\left(1+\frac{r}{100}\right)^n

    Where A is the annuity (the expected return), P the principal (initial amount invested), r is the rate and n is the term (or number of years invested).

    The only question I have is, have you invested for 5 years or 6? If your beginning was the start of year one and the end was the start of year 6 then this would be n= 5 years. If your end point was the end of year 6 then you would have n=6.

    Here is my attempt with n = 5

    You have

    2448.1061 = 1916.4612\left(1+\frac{r}{100}\right)^5

    \frac{2448.1061}{1916.4612} = \left(1+\frac{r}{100}\right)^5

    \sqrt[5]{\frac{2448.1061}{1916.4612}} = 1+\frac{r}{100}

    \sqrt[5]{\frac{2448.1061}{1916.4612}} -1= \frac{r}{100}

    100\times \left(\sqrt[5]{\frac{2448.1061}{1916.4612}} -1\right)= r

    r = 100\times \left(\sqrt[5]{\frac{2448.1061}{1916.4612}} -1\right)

    This will give you the required rate. After you have this you can solve for the next year by substituting the value into r below. (Once again dependant on that start year/end year condition)

    A = 1916.4612\left(1+\frac{r}{100}\right)^6
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  3. #3
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    Quote Originally Posted by valerie142814 View Post
    Hello!

    > I need some help with a growth rate problem (bare with me, I'm bad with math...)

    Should be "bear with me"!
    Your math is not that bad...even pretty good...

    > In year 1, say I have $1916.4612
    > In year 6, I have $2448.1061
    > I have a calculated a CAGR of 4.16%
    > ((1916.4612/2448.1061)^(1/6))-1

    Keerect! Well done.

    > So, if I want to estimate the amount for year 7... can I just take
    > $2448.1061 x 4.16% to get $2550.0690? I'm not sure if that's right...

    Yes...but the multiplication would be 2448.1061 * 1.0416 ; kapish?

    As a matter of fact, that's how the 1916.4612 grew to 2448.1061:
    1916.4612 * 1.0416 * 1.0416 * 1.0416 * 1.0416 * 1.0416 * 1.0416 = 2448.1061
    .
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