The general equation we are working with is $y=ab^x$ where a is the initial value, $b$ is the multiplier, $x$ is the number of times the interest compounds, and $y$ is the amount of money in the account.

Begin by finding the initial value: add the money she already has to the money she is depositing from her birthday gift.

Since the interest is $3.25\%$ annually but it's compounded quarterly, she's going to receive one-fourth of the interest each quarter.

$\frac{1}{4} \cdot 0.0325 = 0.008125$

This number would allow us to find the interest each quarter, but since we want to find how much money she has altogether, we add 1 to that number (1 + 0.008125 = 1.008125) to get the multiplier.

So far the equation looks like this: y = 412.54(1.008125)^x. Since the interest compounds 4 times a year, x = 2 · 4 = 8.

$$440.13$