Example 1: Michael is saving for his retirement and deposits $\$ 5000$ into an investment account at the end of each year for 10 years. The account earns $4 \%$ interest annually. What is the future value of the investment after the $10^{\text {th }}$ deposit?
NOTE: because the payment is made at the END of the period, the geometric series will look different to the above worked solution.

Step 1 ：Given that Michael deposits $5000 into an investment account at the end of each year for 10 years. The account earns 4% interest annually.

Step 2 ：We are asked to find the future value of the investment after the 10th deposit.

Step 3 ：We can use the formula for the future value of an annuity due to solve this problem. The formula is: \(FV = P \times \left[(1 + r)^n - 1\right] / r\)

Step 4 ：In this formula, \(FV\) is the future value of the annuity, \(P\) is the amount of each individual annuity, \(r\) is the interest rate (in decimal form), and \(n\) is the number of periods (in this case, years).

Step 5 ：Substituting the given values into the formula, we get: \(FV = 5000 \times \left[(1 + 0.04)^{10} - 1\right] / 0.04\)

Step 6 ：Solving the above expression, we find that \(FV \approx 60030.54\)

Step 7 ：\(\boxed{\text{The future value of the investment after the 10th deposit is approximately $60,030.54.}}\)