You are investing money at 5.7 percent annual interest, compounded continuously. It will take you how many years to double your investment?
The formula for compount interest is
$\displaystyle A = P(1 + r)^n$.
Here, $\displaystyle r = 5.7\%, A = 2P$
So $\displaystyle 2P = P\left(1 + 5.7\%\right)^n$
$\displaystyle 2 = \left(1 + \frac{5.7}{100}\right)^n$
$\displaystyle 2 = \left(\frac{1057}{1000}\right)^n$
$\displaystyle \ln{2} = \ln{\left[\left(\frac{1057}{1000}\right)^n\right]}$
$\displaystyle \ln{2} = n\ln{\left(\frac{1057}{1000}\right)}$
$\displaystyle n = \frac{\ln{2}}{\ln{\left(\frac{1057}{1000}\right)}}$
$\displaystyle n = \frac{\ln{2}}{\ln{1057} - \ln{1000}}$.
Yeah, it's an online homework problem and the system isn't accepting it, for some reason
WeBWorK : math1050fall2009-1 : 9 : 1
I don't know if you can access that, but thank you so much for the help
Thanks guys, after finding out that formula I was able to solve it like this
if money is invested at percent and compounded continuously, then the factor multiplying the initial investment after years is given by To find the time at which the initial investment is doubled we solve the equation Taking the natural logarithm on both sides and dividing by yields which with our value of percent gives a value of
Still didn't invested but in plane to invest.....
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Compound Interest Formula