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  1. #1
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    help lease

    i have

    r = [1 - ( 1 - 1/Tr)^L ] x 100%

    and i need Tr and i have L = 2 and r = 2%
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by question View Post
    i have

    r = [1 - ( 1 - 1/Tr)^L ] x 100%

    and i need Tr and i have L = 2 and r = 2%
    If your expression is correct we have

    2=(1-(1-1/Tr)^2)*100

    so:

    0.02=1-(1-1/Tr)^2

    bringing the 1 over to the left:

    0.02-1=-(1-1/Tr)^2

    or:

    0.98=(1-1/Tr)^2

    so:

    1-1/Tr=sqrt(0.98) ~= 0.98995

    so

    1/Tr~=1- 0.98995=0.01005

    Tr~=99.5~=100

    RonL
    Last edited by CaptainBlack; January 13th 2007 at 11:18 AM. Reason: add more precission to the calculation
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  3. #3
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by question View Post
    i have

    r = [1 - ( 1 - 1/Tr)^L ] x 100%

    and i need Tr and i have L = 2 and r = 2%
    r = [1 - ( 1 - 1/Tr)^L ] \cdot 100

    \frac{r}{100} = 1 - \left ( 1 - \frac{1}{Tr} \right )^L

    \frac{r}{100} - 1 = - \left ( 1 - \frac{1}{Tr} \right )^L

    1 - \frac{r}{100} = \left ( 1 - \frac{1}{Tr} \right )^L

    (Just a note: I seem to recall doing this before and doing something silly with a "log" term at this point. I don't know why I did it that way, and it may well have been wrong. My apologies if I'm remembering that correctly!)

    \left ( 1 - \frac{r}{100} \right ) ^{1/L} = 1 - \frac{1}{Tr}

    \frac{1}{Tr} = 1 - \left ( 1 - \frac{r}{100} \right ) ^{1/L}

    Tr = \frac{1}{1 - \left ( 1 - \frac{r}{100} \right ) ^{1/L}}

    With r = 2 and L = 2:
    Tr = \frac{1}{1 - \left ( 1 - \frac{2}{100} \right ) ^{1/2}}

    Tr = \frac{1}{1 - \sqrt{\frac{98}{100}}}

    Tr = 99.4975

    -Dan
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