Money Problems

You start with $2500. After each year, you add 4.5% of what you have to what you have. This can be expressed as $m=2500*1.045^y$ . If the amount of money desired is $3500, then set m equal to 3500. Then solve for y.

$3500=2500*1.045^y$

$\frac{3500}{2500}=1.045^y$

$\frac{7}{5}=1.045^y$

$\log_{1.045}^\frac{7}{5} = y$

$7.64416276... = y$

But because the amount is only added after a full year, you round up to $\boxed{8}$