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 $$1,000,$ and the $1-$year and $11-$year spot interest rates are $6\mathrm{.}1$ percent and $8\mathrm{.}1$ percent, respectively. $($Do not round intermediate calculations. Round the final answers to $2$ decimal places. Omit $ sign in your response.

a$.$ What is the forward price of your contract?

Forward price

$ $491\mathrm{.}62$

b$.$ Suppose both the $1-$year and $11-$year spot rates unexpectedly shift downward by $3\mathrm{.}0$ percent. What is the new price of the forward contract?

New forward price

$$627\mathrm{.}16$