$13$:$23$

$-=,\{\begin{array}{ccc}\text{:}[& \text{M}\text{a}\text{y}\text{n}\text{o}\text{o}\text{t}\text{h}& ]\\ & \text{U}\text{n}\text{i}\text{v}\text{e}\text{r}\text{s}\text{i}\text{t}\text{y}& \\ & \text{N}\text{a}\text{t}\text{i}\text{o}\text{n}\text{a}\text{l}\text{U}\text{n}\text{i}\text{v}\text{e}\text{r}\text{i}\text{t}\text{y}& \\ & of\text{r}\text{e}\text{l}\text{a}\text{n}\text{d}\text{M}\text{a}\text{y}\text{n}\text{o}\text{o}\text{t}\text{h}& \end{array}$

Marked out of $1\mathrm{.}00$

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The stock of Pocklingto Time left $0$:$45$:$14$ Pharmaceuticals is trading at $107.$ There is a dividend of $5$ due $3$ months from now. What is the lower bound of a $6-$month European call option written on this stock with a strike price of $100,$ if the riskless rate of interest is $5\%$ with continuous compounding for all maturities?

a$.$ None of the numerical answers are correct.

b$.14\mathrm{.}29$

c$.9\mathrm{.}47$

d$.4\mathrm{.}53$

e$.14\mathrm{.}41$