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

$3\mathrm{.}77\%$

$12$ months

$4\mathrm{.}21$

$18$ months

$4\mathrm{.}89$

$24$ months

$5\mathrm{.}61$

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 $20$ basis points For example, the six$-$month rate increased from $3\mathrm{.}77$ percent to $3\mathrm{.}97$ percent. What is the price of a forward contract otherwise identical to yours given these changes? $($Do not round intermediate calculations and round your answer to $2$ decimal places, e$.$g$.,32\mathrm{.}16.)$