$4.$ Given: C $=$ $$2\mathrm{.}50,$ P $=$ $$4\mathrm{.}99,$ S $=$ $$26\mathrm{.}84,$ K $=$ $$30,$ T $=3$ months, r $=4\%$

a$.$ What would you do to exploit these quotes? $($List the transactions.$)$

b$.$ What would be your riskless arbitrage profit?

c$.$ How could you synthetically lend money risk$-$free using only stock options and the purchase or sale of stock?

d$.$ What is the implied interest rate on the synthetic loan in $($c$)?$ Would you be better off lending at the $3-$month T$-$Bill rate of $4\%$ p$.$a$.,$ or synthetically lending using options?