## Real World Applications – Algebra I

### Topic

How do banks help you earn money?

### Student Exploration

One way for people to earn a little bit of money is by putting it in a special bank account and letting the bank hold on to it for a long time. Many use a special formula to compound interest:

\begin{align*}A = P\left(1 + \frac{r}{n}\right)^{(nt)}\end{align*}

The \begin{align*}P\end{align*} represents the initial amount of money that’s put into the bank account. The \begin{align*}r\end{align*} represents the interest rate in which the bank will give. The \begin{align*}n\end{align*} represents how often the amount is compounded over time, and \begin{align*}t\end{align*} represents the number of years that the money will be in the bank account for.

For example, I put $5,000 into a bank account for my newborn daughter’s college fund. This bank account offers a 5% interest rate, and is compounded monthly. I’d like for my daughter to get this money by the time she’s 18 and ready for college. With this information, we can calculate how much money she will have by the time she gets to college in 18 years.

\begin{align*}A &= P\left(1 + \frac{r}{n}\right)^{(nt)}\\ A &= 5000\left(1+\frac{.05}{12}\right)^{(12 \times 18)}\end{align*}

We can put all of this into our scientific or graphing calculator! This is what I’ve entered:

\begin{align*}& 5000\left(1+\left(\frac{.05}{12}\right)\right)^{(12 \times 18)}\\ & = 12275.04\end{align*}

This means that the bank will have accumulated $12,275 by the time she graduates high school.

### Extension Investigation

Look into different banks and find out their compounding interest rate. Make up an amount that you would think of putting into the bank, and find out how much you would have in a specific period of time. This could be a way for you to save money!