#$1$ If the $3-$ and $6-$month simple interest rates are $5\%$ and $5\mathrm{.}5\%,$ respectively, and a $36$ FRA is available at $5\mathrm{.}5\%,$

determine how much arbitrage profit can be made in $6$ months' time, assuming a FRA nominal of R$1000.$

#$2$ On $21$ December $2022,$ bank A shorts R$200$ million $3$x$6$s at $5\mathrm{.}95\%.$ The $6-$month deposit rate is $6\mathrm{.}07\%.$ Calculate

the following:

$($a$)$ the dates of the near and far legs of the FRA;

$($b$)$ calculate how much the bank would gain or lose if the $6-$month deposit rate increased from $6\mathrm{.}07\%$ to $6\mathrm{.}17\%$

and the $3-$month deposit rate decreased by $5$ bps;

$($c$)$ Assuming the FRA settles in advance, calculate the payoff$/$settlement due to the bank if $3-$month JIBAR

resets at $5\mathrm{.}15\%.$