Find the amount of the payment to be made into a sinking fund so that enough will be present to accumulate the following amount. Payments are made at the end of each period. $\$ 65,000$; money earns $6 \%$ compounded semiannually for $1 \frac{1}{2}$ years

Step 1 ：Recall the formula for the future value of an ordinary annuity: $A = P \times \left[\frac{(1 + r/n)^{nt} - 1}{r/n}\right]$, where $A$ is the end balance, $P$ is the payment made each period, $r$ is the interest rate, $t$ is the number of years, and $n$ is the number of times the interest is compounded in a year.

Step 2 ：Substitute the given values into the formula: $65,000 = P \times \left[\frac{(1 + 0.06/2)^{2 \times 1.5} - 1}{0.06/2}\right]$.

Step 3 ：Solving for $P$ gives $P = 65,000 / \left[\frac{(1 + 0.06/2)^{2 \times 1.5} - 1}{0.06/2}\right] = 21191.68...$

Step 4 ：Rounding to the nearest dollar gives $\boxed{\$21192}$.