Question 255702
Remember that the formula for compound interest is:

{{{A = P(1 + r/n)^nt}}}

In this problem, P = 2500, r = 0.075, n = 4 and t is our unknown.  If Anne earns $500 in interest, then the total amount she has is A = 3000.  So our problem is:

{{{3000 = 2500(1 + 0.075/4)^(4t)}}}

Our first step is to divide both sides by 2500.

{{{1.2 = (1.01875)^(4t)}}}

Now, we need to get the exponent down since that is where the variable is.  So we take the log of both sides:

{{{log(1.2) = (4t)log(1.01875)}}}

Now we divide both sides by log(1.01875):

{{{log(1.2)/log(1.01875) = 4t}}}

And last, we divide both sides by 4:

{{{log(1.2)/(4log(1.01875)) = t}}}

Using the calculator, we have that t = 2.45 years.