a$)$ The S&P$/$ASX $200$ Index $($ie the physical market$)$ is trading at $7315\mathrm{.}202.$ Price the

September SPI$200$ futures contract, which has $86$ days to expiry, when the continuously compounded risk free rate of return is $3\mathrm{.}5850\%,$ the dividend yield on the S&P$/$ASX $200$ Index is $4\mathrm{.}15\%$pa$,$ and custody costs $($ie the cost of holding

physical shares$)$ are $0\mathrm{.}22\%$pa $(1$ mark$)$

$($b$)$ How much profit or loss would you make if you went long $6090-$day bank bill futures contracts at $96\mathrm{.}35$ and closed them out $27$ days later at $96\mathrm{.}08$ when the continuously compounded risk free rate is $3\mathrm{.}5850\%?$