This morning you agreed to buy a one$-$year Treasury bond in six months. The bond has a face value of $$1,000.$ Use the spot interest rates listed here to answer the following questions.

Time EAR

$6$ months $3\mathrm{.}65\%$

$12$ months $4\mathrm{.}09$

$18$ months $4\mathrm{.}77$

$24$ months $5\mathrm{.}49$

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

b$.$ Suppose shortly after you purchased the forward contract all rates increased by $40$ basis points. For example, the six$-$month rate increased from $3\mathrm{.}65$ percent to $4\mathrm{.}05$ percent. What is the price of a forward contract otherwise identical to yours given these changes? $($Do