Dudley Savings Bank wishes to take a position in Treasury bond futures contracts, which currently have a quote of $107100.$ Dudley Savings thinks interest rates will go down over the period of investment. The face value of the bond underlying the futures contract is $$100,000.$

a$.$ Should the bank go long or short on the futures contracts?

b$.$ Given your answer to part $($a$),$ calculate the net profit to Dudley Savings Bank if the price of the futures contracts increases to $107220.($Negative amount should be indicated by a minus sign. Do not round intermediate calculations. Round your answer to $2$ decimal places. $($e$.$g$.,32\mathrm{.}16))$

c$.$ Given your answer to part $($a$),$ calculate the net profit to Dudley Savings Bank if the price of the futures contracts decreases to $106280$