help lease

• Jan 13th 2007, 09:16 AM
question
help lease
i have

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

and i need Tr and i have L = 2 and r = 2%
• Jan 13th 2007, 09:51 AM
CaptainBlack
Quote:

Originally Posted by question
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
• Jan 13th 2007, 10:02 AM
topsquark
Quote:

Originally Posted by question
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