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 $5\mathrm{.}5$ percent and $7\mathrm{.}5$ 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 $1$

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$.,32\mathrm{.}16.)$