ARC Resources has just entered into a forward rate agreement $($FRA$)$ with BMO whereby the

latter agreed to lend $$55$ million to the former for an $18-$month period, effective six months from

now. BMO posts the following lending rates $($all continuously compounded in annual terms$)$:

a$)$ What should be the fair contract rate? What if the actual, signed contract rate is $3\mathrm{.}9095\%$

instead? What is the value of the contract to ARC Resources?

b$)$ Supposing that right after the signing of the FRA with BMO, ARC Resources observes the

following lending rates from Scotia $($all continuously compounded in annual terms$)$:

Should ARC Resources have signed the FRA with Scotia instead? How much is the dollar

difference in today's terms between the two RFA's $($assuming ARC Resources signed at

$3\mathrm{.}9095\%$

Please keep four decimal places in the percentage numbers, e$.$g$.,3\mathrm{.}9654\%$