Question 178415
Ok, so we know that P=100, r=0.02, n=4 and we want A=125.  So the question is to solve for t.
{{{125=100(1+0.02/4)^(4t)}}}
The first thing I will do is divide both sides by 100.
{{{1.25=(1+0.005)^(4t)}}}
Now, since the variable is an exponent, we need to use logarithms so we can get the exponent down.  So I will take the log of both sides.
{{{log(1.25)=log(1.005^(4t))}}}
{{{log(1.25)=4tlog(1.005)}}}
So,
{{{t=log(1.25)/4log(1.005)}}}
Thus,
{{{t=11.185}}}
So, depending on how you are supposed to round, it will take her 11.2 years to reach $125, or if you are supposed to round to the year, it would be 12 years.  Now, for doubling, that would mean we want A=200.  So you do the same exact steps with A=200 instead of 125.