Starting six months after her grandson Robin's birth, Mrs. Devine made deposits of $\mathrm{\$}160$ into a trust fund every six months until Robin was twenty-one years old. The trust fund provides for equal withdrawals at the end of each six months for five years, beginning six months after the last deposit. If interest is $5.74\mathrm{\%}$ compounded semi-annually, how much will Robin receive every six months?
Robin will receive $\mathrm{\$}$ (Round the final answer to the nearest cent as needed. Round all intermediate values to six decimal places as needed.)

Step 1 ：First, we calculate the future value of the deposits made by Mrs. Devine using the formula for the future value of an ordinary annuity: $FV=P\times [(1+\frac{r}{n}{)}^{nt}-1]÷\frac{r}{n}$, where $P=\mathrm{\$}160$, $r=5.74\mathrm{\%}$, $n=2$, and $t=21$ years.

Step 2 ：Next, we calculate the present value of the withdrawals that Robin will receive using the formula for the present value of an ordinary annuity: $PV=C\times [1-(1+\frac{r}{n}{)}^{-nt}]÷\frac{r}{n}$, where $C$ is the cash flow per period (which we are trying to find), $r=5.74\mathrm{\%}$, $n=2$, and $t=5$ years.

Step 3 ：We know that the present value of the withdrawals should be equal to the future value of the deposits, so we set the two equations equal to each other and solve for $C$.

Step 4 ：Finally, we find that Robin will receive approximately $\boxed{{\displaystyle \mathrm{\$}1481.47}}$ every six months.