Dana’s mother gave her
The general equation we are working with is
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
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.