Find the future value. $\$ 52,161$ invested for 8 years at $4 \%$ compounded semiannually

Step 1 ：We are given that the principal amount (P) is $52,161, the annual interest rate (r) is 4% or 0.04 in decimal form, the number of times that interest is compounded per year (n) is 2 (since it's compounded semiannually), and the time the money is invested for (t) is 8 years.

Step 2 ：We can find the future value of the investment using the formula for compound interest: \(FV = P * (1 + r/n)^{nt}\)

Step 3 ：Substituting the given values into the formula, we get \(FV = 52161 * (1 + 0.04/2)^{2*8}\)

Step 4 ：Solving the equation, we find that the future value of the investment is approximately $71,605.88

Step 5 ：\(\boxed{71605.88}\) is the future value of the investment.