$3.$ Consider a bank that has made a three$-$month Eurodollar loan of $$3,000,000$ against an offsetting six$-$month Eurodollar deposit. The bank$$s concern is that three$-$month LIBOR will fall below expectations and the Eurocredit is rolled over at the new lower base rate, making the six$-$month deposit unprofitable. To protect itself, the bank could use FRA and Eurodollar futures contact.

$1)$ Assume Agreement Rate is $6\%$ and the actual number of days in the three$-$month FRA period is $91.$

a$)$ What position $($buy or sell$)$ should the bank take?

b$)$ Suppose the three$-$month market LIBOR turns out to be $5\mathrm{.}125\%,$ what is the amount of cash settlement? When?

c$)$ What is the effective lending rate in three months?

$2)$ Assume that the bank can take a position in Eurodollar futures contracts that mature in three months and have a futures price of $94\mathrm{.}00.$

a$)$ What position should the bank take $($long or short$)?$

b$)$ How many contracts are needed?