Currently everyone in the market is able sell or purchase risk$-$free bond of any par value and earn$/$pay an interest rate of $5\%.$

Consider the prices of options on one share of Stock Y$,$ which has a current market price of $$40.$

Call Option: Strike Price $$35\mathrm{.}00$; Premium $$8\mathrm{.}13$

Call Option: Strike Price $$37\mathrm{.}50$; Premium $$5\mathrm{.}80$

Call Option: Strike Price $$40\mathrm{.}00$; Premium $$4\mathrm{.}90$

Call Option: Strike Price $$42\mathrm{.}50$; Premium $$4\mathrm{.}00$

Call Option: Strike Price $$45\mathrm{.}00$; Premium $$3\mathrm{.}20$

Put Option: Strike Price $$35\mathrm{.}00$; Premium $$1\mathrm{.}46$

Put Option: Strike Price $$37\mathrm{.}50$; Premium $$2\mathrm{.}86$

Put Option: Strike Price $$40\mathrm{.}00$; Premium $$3\mathrm{.}00$

Put Option: Strike Price $$42\mathrm{.}50$; Premium $$4\mathrm{.}00$

Put Option: Strike Price $$45\mathrm{.}00$; Premium $$5\mathrm{.}66$

Round your calculations to the nearest $$0\mathrm{.}01.$

Identify all the arbitraging opportunities given in the option premiums. Consider only arbitraging opportunities that will provide a profit of more than $$0\mathrm{.}01/$share right away.

For each of the arbitraging opportunity you find, explain what need to be done to profit from the opportunity and calculate the size of profits to be made right now.