You have built the following interest rate tree for the next $3$ years:

Time $1(\%)$ Time $2(\%)$ Time $3(\%)$

i$3$hh $=5\mathrm{.}79$

i$2$h $=3\mathrm{.}55$

i$1=2\mathrm{.}63$ i$3$hl $=$ i$3$lh $=4\mathrm{.}09$

i$2$l $=3\mathrm{.}07$

i$3$ll $=3\mathrm{.}23$

You are interested in valuing a $3$ year floating rate bond with coupon rate set in arrears at a credit spread of $69$ bps$.$ The coupon is capped at $4\mathrm{.}5\%,$ and floored at $3\mathrm{.}17\%.$

What is the value of this bond per $$100$ of par value?