Question $2$: Forwards on Stocks $(2/10)$ Suppose a share in HKUST currently trades for $$100$ now and the risk free interest rate is $5\%($annual$,$ continuously compounded$).$ There is a forward contract that allows you to purchase one HKUST share in $18$ months.

$(1)$ What is the $18-$month forward price of one HKUST share?

$(2)$ Suppose HKUST announces $2$ dividend payments of $$1$ per share in exactly $9$ and $18$ months, and assume that HKUST stock price does not change upon the announcement, what must be the new $18-$month forward price of the share?

$(3)$ If after the dividend announcement, the $18-$month forward price still stays the same, how would you make arbitrage profit from the market mis$-$pricing?

$(4)$ Instead, suppose HKUST announces a dividend yield of $1\%($annual$,$ continuously compounded$),$ and assume that HKUST stock price does not change upon the announcement, what must be the new $18-$month forward price of the share?