$1)$ In a one$-$period binomial model, assume that the current stock price is $$100,$ and that it will rise to $$130$ or fall to $$70$ after one month. The gross one month risk$-$free rate is $1\mathrm{.}02\%.$ Using risk neutral pricing, what is the price of a $100$strike one$-$month call option? Round your calculaton for q and $1$ q to four $(4)$ decimal places.

a$.$ $$14\mathrm{.}90$

b$.$ $$14\mathrm{.}71$

c$.$ $$15\mathrm{.}05$

d$.$ $$15\mathrm{.}69$

$2)$ In a one$-$period binomial model, assume that the current stock price is $$100,$ and that it will rise to $$120$ or fall to $$80$ after one month. The gross one month risk$-$free rate is $1\mathrm{.}03\%.$ Using risk neutral pricing, what is the price of a $100$strike one$-$month put option? Round your calculaton for q and $1$ q to three $(3)$ decimal places

a$.$ $$8\mathrm{.}00$

b$.$ $$8\mathrm{.}25$

c$.$ $$8\mathrm{.}50$

d$.$ $$8\mathrm{.}75$