\begin{tabular}{l|l}\( \begin{array}{l}\text { Suppose that you earned a bachelor's degree } \\ \text { and now you're teaching high school. The }\end{array} \) & \( \begin{array}{l}\text { a. After } 5 \text { years, you will have } \\ \text { school district offers teachers the opportunity }\end{array} \) \\ \( \begin{array}{l}\text { approximately } \$ \square . \\ \text { to take a year off to earn a master's degree. } \\ \text { To achieve this goal, you deposit } \$ 1000 \text { at the } \\ \text { end of each year in an annuity that pays } 6 \%\end{array} \) & \( \begin{array}{l}\text { (Do not round until the final answer. } \\ \text { Then round to the nearest dollar } \\ \text { compounded annually. } \\ \text { as needed.) }\end{array} \) \\ \( \begin{array}{ll}\text { a. How much will you have saved at the end } \\ \text { of five years? }\end{array} \) & \\ b. Find the interest. \end{tabular}

To calculate how much you'll have saved at the end of five years with a deposit of $1000 at the end of each year into an annuity that earns 6% interest compounded annually, we can use the future value of an ordinary annuity formula: \[ FV = P \times \frac{(1 + r)^n - 1}{r} \] Where \( P = 1000 \), \( r = 0.06 \), and \( n = 5 \). Plugging in these values: \[ FV = 1000 \times \frac{(1 + 0.06)^5 - 1}{0.06} \approx 1000 \times \frac{1.338225 - 1}{0.06} \approx 1000 \times 5.63766 \approx 5637.66 \] So, at the end of five years, you will have approximately $5638 saved (rounding to the nearest dollar). Now, to find the interest earned, you take the total savings and subtract the total amount contributed. The total contribution is \( 5 \times 1000 = 5000 \). Therefore, the interest earned is: \[ 5638 - 5000 = 638 \] At the end of five years, you will have saved approximately $5638, with $638 being the interest earned.