Suppose that, in a Treasury bond futures contract, it is known that the cheapest-to-deliver bond will be a 12% coupon bond with a conversion factor of 1.t000 (I.e. the bond will pay $6 coupon on each coupon date.) Suppose also that it is known that delivery will take place in 270 days. The last coupon date was 6x days ago. The next coupon date is in 12y days from today and coupon thereafter is in 30z days from today. The term structure is flat, and the continuously compounded rate of interest is 1t%. Current quoted price of the bond is $115. Calculate the quoted futures price after conversion. Make sure you use at least 6 decimals in your calculations.

x=5, y=3, z=6, t=5