Find the amount of each payment to be made into a sinking fund earning $5 \%$ compounded monthly to accumulate $\$ 92,000$ over 9 years. Payments are made at the end of each period. The payment size is $\$ \square$. (Round to the nearest cent.)

Step 1 ：We are given the future value (FV), the interest rate (r), and the number of periods (n). We need to find the payment size (PMT). The formula for the future value of an ordinary annuity can be rearranged to solve for PMT: \(PMT = \frac{FV}{(1 + \frac{r}{n})^{nt} - 1} \times \frac{r}{n}\)

Step 2 ：Where: \(FV = 92000\), \(r = 0.05\), \(n = 12\), and \(t = 9\)

Step 3 ：Substitute the given values into the formula: \(PMT = \frac{92000}{(1 + \frac{0.05}{12})^{12 \times 9} - 1} \times \frac{0.05}{12}\)

Step 4 ：Solving the equation gives: \(PMT = 676.26\)

Step 5 ：Final Answer: The payment size is \(\boxed{676.26}\)