Suppose that you earned a bachelor's degree and now you're teaching high school. The school district offers teachers the opportunity to take a year off to earn a master's degree. To achieve this goal, you deposit \( \$ 3000 \) at the end of each year in an annuity that pays \( 4.5 \% \) compounded annually. a. How much will you have saved at the end of five years? b. Find the interest.
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To calculate how much you'll have saved at the end of five years with your annuity, you can use the future value of an ordinary annuity formula: \[ FV = P \times \frac{(1 + r)^n - 1}{r} \] Where: - \( FV \) = future value of the annuity - \( P \) = annual payment (\$3000) - \( r \) = annual interest rate (4.5% or 0.045) - \( n \) = number of years (5) Plugging in the numbers: \[ FV = 3000 \times \frac{(1 + 0.045)^5 - 1}{0.045} \approx 3000 \times \frac{1.24623 - 1}{0.045} \approx 3000 \times 5.46627 \approx 16398.81 \] So, at the end of five years, you will have saved approximately **\$16,398.81**. Now for the interest earned, you simply subtract the total contributions from the future value: Total contributions over 5 years = \( 3000 \times 5 = 15000 \) Interest earned = \( FV - \text{Total Contributions} = 16398.81 - 15000 \approx 1398.81 \) So, the interest earned over 5 years is approximately **\$1,398.81**.