Sorenson Corp.$\text{'}$s expected year$-$end dividend is $D_1=$$$2\mathrm{.}30,$ its required return is $r_s=14\mathrm{.}00\%,$ its dividend yield is $6\mathrm{.}00\%,$ and its growth rate is expected to be constant in the future. What is Sorenson's expected stock price in $5$ years, i$.$e$.,$ what is tilde$(P{)}_5?$ Do not round intermediate calculations.

a$.$ $$41\mathrm{.}40$

b$.$ $$73\mathrm{.}81$

c$.$ $$56\mathrm{.}32$

d$.$ $$51\mathrm{.}30$

e$.$ $$52\mathrm{.}15$