Assume S $=$ $$31\mathrm{.}75,$ div $=0,$ r$=0\mathrm{.}03,$ and sigma $=0\mathrm{.}20,$ and $90$ days until the expiration of a standard call option. A call on call compound option with an exercise price of $$2\mathrm{.}00$ has $180$ days until expiration. What is the premium of the call on call option? a$)$ $$1\mathrm{.}46,$ b$)$ $$2\mathrm{.}46,$ c$)$ $$3\mathrm{.}04,$ d$)$ $$3\mathrm{.}53$ Why is the correct answer A$?$ Show with formulas.