Given the following two sets of cash flows:

Option A: $$29,801\mathrm{.}47$ in $2$ years plus $$Y$ in $11$ years time.

Option B: $$69,587\mathrm{.}285$ years from today.

The nominal rate $i^{(365)}=3\mathrm{.}227\%$ makes the present value of these two options the same. What is the value of $Y?$

a$.$ $$47,731\mathrm{.}32$

b$.$ $$44,608\mathrm{.}71$

c$.$ $$47,285\mathrm{.}23$

d$.$ $$45,946\mathrm{.}97$

e$.$ $$46,839\mathrm{.}15$