Assume the riskless rate is $3\mathrm{.}8\%.$ A stock sells for $$85,$ and in one year it will either in value to $$100$ or fall in value to $$70.$

a$.(7$ points$)$ Find the value of a $$85$ call using the binomial model.

b$.(6$ points$)$ Calculate the value of the call using risk neutral valuation.

c$.(10$ points$)$ Calculate the value of a $$85$ put using both the binomial model and put$-$call parity.