It is May $1.$ The quoted price of a bond with an Actual$/$Actual $($in period$)$ day count and $9\%$ per annum coupon $($paid semiannually$)$ in the United States is $102.$ It has a face value of $100$ and pays coupons on April $1$ and October $1.$ What is the cash price? $($Round to two decimal places$).$

Hint: There are $30$ days between April $1$ and May $1$ and $183$ days between April $1$ and October $1$

$$101\mathrm{.}50$

$$102\mathrm{.}74$

$$103\mathrm{.}55$

$$105\mathrm{.}98$