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Thread: Calculating the result of a 5% growth rate over ten years

  1. #1
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    Calculating the result of a 5% growth rate over ten years

    Hi,

    I am curious how I can calculate the total value of an investment if it is expected to grow at 5% annually over the next 10 years.

    Right now, assets are at 13.8 trillion and are expected to grow at 5% over the next ten years. What I tried to do was 13.8*0.05=0.69, 0.69*10=6.9, 13.8+6.9=20.7. However, this is wrong, the answer is actually 22.5 trillion and I have no idea why.

    Thanks.

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    Quote Originally Posted by pc510 View Post
    Hi,

    I am curious how I can calculate the total value of an investment if it is expected to grow at 5% annually over the next 10 years.

    Right now, assets are at 13.8 trillion and are expected to grow at 5% over the next ten years. What I tried to do was 13.8*0.05=0.69, 0.69*10=6.9, 13.8+6.9=20.7. However, this is wrong, the answer is actually 22.5 trillion and I have no idea why.

    Thanks.
    Have you considered compounded growth?

    Suppose the growth rate is 10% and you start with $1000.

    At the end of the first year you would have (1000 + 10% of 1000 =) $1100

    At the end of the second year you would have (1100 + 10% of 1100 =) $1210

    At the end of the third year you would have (1210 + 10% of 1210 =) $1331

    You'll need to account for "interests" earning "interest"!!
    “... mathematics is only the art of saying the same thing in different words” - B. Russell

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    F = P(1 + i)^n
    where:
    P = Present value (13.8)
    i = interest (.05)
    n = number of years (10)
    F = Future value (?)
    I'm just an imagination of your figment !

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    Dennis,

    Thanks for the formula. This is very helpful. I didn't realize I should be using F=P(1+i)^n.

    I have a follow up question. This is quite easy to do with a calculator, but if I were to do this by hand, is there any way to calculate the 1.05^10 how would I do that?

    Thank you again!

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    Elite Member stapel's Avatar
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    Cool

    Quote Originally Posted by pc510 View Post
    ...if I were to do this by hand, is there any way to calculate the 1.05^10 how would I do that?
    Multiply 1.05 by 1.05 by 1.05 by 1.05 by 1.05 by 1.05 by 1.05 by 1.05 by 1.05 by 1.05, just like the exponent tells you to!

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    Quote Originally Posted by pc510 View Post
    I have a follow up question. This is quite easy to do with a calculator, but if I were to do this by hand, is there any way to calculate the 1.05^10 how would I do that?
    WHY d'heck would you want to do that?
    If your teacher expects such manual calculations,
    then you and your classmates should get him/her fired
    I'm just an imagination of your figment !

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    Quote Originally Posted by pc510 View Post
    I have a follow up question. This is quite easy to do with a calculator, but if I were to do this by hand, is there any way to calculate the 1.05^10 how would I do that?
    In the days before calculators, we would probably have done this with a slide rule, or with a table of logarithms. Before there were logarithms, there were similar methods using trig tables. In some countries, students still use log tables.

    There are also ways to make repeated multiplication a little more efficient, if you had to do it entirely by hand. You might do this:

    1.05^2 = 1.1025
    1.05^4 = 1.1025^2 = 1.2155 (rounded)
    1.05^8 = 1.2155^2 = 1.4774 (rounded)
    1.05^10 = 1.05^8 * 1.05^2 = 1.4774*1.1025 = 1.6288 (rounded)

    compared to the actual value, 1.62889462677744140625. That took only four multiplications.

    Of course, that's mostly for historical interest; but in fact logs might be what you would be using in a computer program, and the last method, called by various names such as "binary exponentiation", is also used in computing.

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