An FRN has a face value of $$1.$ The first coupon payment is $4\mathrm{.}75\%.$The first coupon payment at initiation is $182$ days.

It has four remaining payment dates:

Time to payment Libor rates as of t$0$

t$1=90$ days $5\mathrm{.}35\%$

t$2=273$ days $6\mathrm{.}58\%$

t$3=455$ days $6\mathrm{.}40\%$

t$4=638$ days $5\mathrm{.}95\%$

What is the value of the FRN$?$

Question $3$ options:

$1\mathrm{.}015$

$1\mathrm{.}010$

$1\mathrm{.}038$

$1\mathrm{.}117$