It is July $30,2022.$ The cheapest$-$to$-$deliver bond $($for a September $2022$ Treasury bond futures contract$)$ is a $6\%$ coupon bond, and delivery is expected to be made on September $30,2022.$ Coupon payments on the bond are made on February $30$ and August $30$ each year. The term structure is flat, and the discount rate with semiannual compounding is $2\%$ per annum. The conversion factor for the bond is $1\mathrm{.}4.$ The current quoted bond price is $$105.$ Calculate the quoted futures price for the contract.