You enter into a forward contract to buy a $10-$year, zero coupon bond that will be issued in one year. The face value of the bond is $$1,000$ and the $1-$year and $11-$year spot interest rates are $6\mathrm{.}5$ percent and $8\mathrm{.}5$ percent, respectively.

a$.$ What is the forward price of your contract? $($Do not round intermediate calculations and round your answer to $2$ decimal places, e$.$g$.,32\mathrm{.}16.)$

b$.$ Suppose both the $1-$year and $11-$year spot rates unexpectedly shift downward by $1\mathrm{.}5$ percent. What is the new price of the forward contract? $($Do not round intermediate calculations and round your answer to $2$ decimal places, e$.$g$.,32\mathrm{.}16.)$