Assume that the $6-$month futures contract on SPX settled at $4047,$ r $=3\mathrm{.}75\%,$

q $=1\mathrm{.}75\%,$ arbitrage transactions costs $($TC$)$ are $1\mathrm{.}16$ index points. The TC band is $[4053\mathrm{.}48,4051\mathrm{.}16].$ The Fair Value of the Futures contract is

a$.4047\mathrm{.}00$

b$.4042\mathrm{.}57$

c$.3971\mathrm{.}88$

d$.4052\mathrm{.}32$

e$.$ If none of the above, provide your solution