Yize Chen trades currencies for Sumatra Funds in Jakarta. She focuses nearly all of her time and attention on the U$.$S$.$ dollar $($USD$)$ to Singapore dollar $($SGD$)$ cross$-$rate. The current spot rate is USD$0\mathrm{.}6000=$ SGD$1\mathrm{.}00.$ After considerable study, she has concluded that the Singapore dollar will appreciate versus the U$.$S$.$ dollar in the coming $90$ days, probably to about USD$0\mathrm{.}7000=$ SGD$1\mathrm{.}00.$ She has the following options on the Singapore dollar to choose from:

Option Strike Price Premium

Put on SGD USD$0\mathrm{.}6500=$SGD$1\mathrm{.}00$ USD$0\mathrm{.}00003$ per SGD

Call on SGD USD$0\mathrm{.}6500=$SGD$1\mathrm{.}00$ USD$0\mathrm{.}00046$ per SGD

a$.$ Should Yize buy a put on Singapore dollars or a call on Singapore dollars?

b$.$ What is Yize's break$-$even price on the option purchased in part $($a$)?$

c$.$ Using your answer from part $($a$),$ what is Yize's gross profit and net profit $($including premium$)$ if the spot rate at the end of $90$ days is indeed USD$0\mathrm{.}7000=$ SGD$1\mathrm{.}00?$

d$.$ Using your answer from part $($a$),$ what is Yize's gross profit and net profit $($including premium$)$ if the spot rate at the end of $90$ days is USD$0\mathrm{.}8000=$ SGD$1\mathrm{.}00?$