uestion $3$: The Value of A Forward Contract $(2/10)$ Suppose a share in HKUST currently trades for $$100$ on Jan $1$st and the risk free interest rate is $10\%($annual$,$ continuously compounded$).$ There is a forward contract that allows you to purchase one HKUST share in Jul $1$st$.$

$(1)$ What is the forward price?

$(2)$ What is the value of the forward contract now on Jan $1$st$?$

$(3)$ Suppose after $3$ months $($on Apr $1$st$),$ the price of one HKUST share stays at $$100.$ Then, on April $1$st$,$ what is the forward price of a forward contract with delivery date on Jul $1$st$.$

$(4)$ Following $(3),$ on Apr $1$st$,$ what is the value of the original forward contract $($the one you entered on Jan $1$st$)?$

$(5)($Optional$)$ Suppose after $3$ months $($on Apr $1$st$),$ the price of one HKUST share increases to $$110.$ Then, on April $1$st$,$ what is the value of the short position on the original forward contract $($the one you entered on Jan $1$st$)?$