Use the following formula, where $P$ is the present value of $A$ dollars $t$ years from now, earning annual interest $\mathrm{r}$ compounded $\mathrm{n}$ times per year. \[ P=A\left(1+\frac{r}{n}\right)^{-n t} \] Find the present value of $\$ 500,00015$ years from now, if interest is compounded semiannually at $9.6 \%$. The present value is approximately $\$ \square$. (Round to the nearest hundred as needed.)

Step 1 ：We are given the formula for calculating the present value of an amount of money: \(P=A\left(1+\frac{r}{n}\right)^{-n t}\)

Step 2 ：We are also given the values for \(A\), \(t\), \(r\), and \(n\): \(A = 500000\), \(t = 15\), \(r = 0.096\), and \(n = 2\)

Step 3 ：We can substitute these values into the formula: \(P=500000\left(1+\frac{0.096}{2}\right)^{-2 \times 15}\)

Step 4 ：Calculating the above expression gives us the present value: \(P = 122498.71271207105\)

Step 5 ：Rounding to the nearest hundred as needed, we get the final answer: \(\boxed{\$122,498.71}\)