  ### Home > CCA2 > Chapter Ch5 > Lesson 5.1.2 > Problem5-36

5-36.

Dana’s mother gave her $\175$ on her sixteenth birthday. “But you must put it in the bank and leave it there until your eighteenth birthday,” she told Dana. Dana already had $\237.54$ in her account, which pays $3.25\%$ annual interest, compounded quarterly. If she adds her birthday money to the account, how much money will she have on her eighteenth birthday if she makes no withdrawals before then? Justify your answer.

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