Question 1203682
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Refer to the steps tutor @Edwin has provided to determine that r = 0.09 = 9% approximately. 


Another approach would be to find the positive root of the function {{{f(x)=7.10(1+x)^(12)-20.08}}}
Use a graphing tool like a TI83/TI84, Desmos, or GeoGebra. 
The root finding feature quickly locates the positive x intercept to be roughly x = 0.09


Then we can use the <a href="https://en.wikipedia.org/wiki/Rule_of_72">rule of 72</a> shortcut.
We divide 72 over the r value, in which we have removed the percent sign. Do not use the decimal form.


doubling time = 72/(r value without percent sign) 
doubling time = 72/9 
doubling time = 8 years


This shortcut gives us an approximation rather than the exact answer. 
But sometimes all that's needed is a good enough approximation.


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A more accurate doubling time formula is
{{{t = (ln(2))/(ln(1+r))}}}
where the 2 in ln(2) refers to doubling. 
Replace 2 with 3 if you want to know how long it takes for your money to triple for instance.


If r = 0.09, then we'll get the following doubling time
{{{t = (ln(2))/(ln(1+r))}}}


{{{t = (ln(2))/(ln(1+0.09))}}}


{{{t = 8.0432}}} approximately, which is fairly close to t = 8 we got earlier.
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