$2).$ Suppose that today is Tuesday, October $1,2024,$ and you have a loan of $$5,000,000$ outstanding, on which you will have to make a floating$-$rate interest rate payment on Monday, October $7.$ The interest payment is determined based on a $3-$month SOFR rate on that day. You fear that in the next several days the rate might rise. So$,$ you hedge yourself by trading $3-$month SOFR futures. Assume that you enter the position at the close of day on Tuesday, October $1,$ and you trade AUG $24$ contract.

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a$.$ In order to hedge yourself, which position in AUG $243-$month SOFR futures will you take $($i$.$e$.$ buy or sell, and the number of contracts$)?$

a$.$ What is your daily gain or loss on your futures position $($on Wednesday, Thursday, Friday, and Monday$)?$

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b$.$ What is the interest rate payment that you have to make on Monday, October $7,$ on your $$5,000,000$ loan?

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c$.$ What is the net cost to you, taking into account the gains$/$losses on your hedge, plus the interest payment on the loan $($ignore the time value of money$)?$