You are given the following data for $3-$month SOFR futures on Wednesday, February $28$:

Month Open High Low Last Change Settle Estimated

Volume Prior Day

Open Interest

DEC $2394\mathrm{.}647594\mathrm{.}647594\mathrm{.}637594\mathrm{.}6450+\mathrm{.}007594\mathrm{.}6475249,8391,122,141$

JAN $2494\mathrm{.}652594\mathrm{.}652594\mathrm{.}650094\mathrm{.}6525+\mathrm{.}007594\mathrm{.}65502416,507$

a$)$ John Jones wants to hedge a floating rate interest payment on a $$3\mathrm{.}8$ million loan. The next quarterly interest payment is determined according to a $3-$month SOFR on Friday, March $1,2024.$ How could he use Dec $233-$month SOFR futures to do it $($position$,$ number of contracts$)?$

b$)$ If he entered the futures position on Monday, February $26,$ at a settle price of $94\mathrm{.}6650.$ What is his cash flow due to marking to market on Tuesday and on Wednesday?

c$)$ If on Friday, March $1,2024,$ the $3-$month SOFR turns out to be $5\mathrm{.}4\%$ p$.$a$.,3-$month SOFR futures price $94\mathrm{.}715$ what would be the total cost to John Jones taking into account gains$/$losses on his hedge, plus the interest payment?

d$)$ What is the effective interest rate?