An FRN has four remaining payment dates:

Time to payment Libor rates as of t$0$

t$1=120$ days $5\mathrm{.}95\%$

t$2=303$ days $5\mathrm{.}98\%$

t$3=485$ days $5\mathrm{.}90\%$

t$4=668$ days $5\mathrm{.}90\%$

The FRN has a face value of $$1.$ The first coupon payment is $6\mathrm{.}25\%..$ What is the value of the FRN$?(182$ days from initiation to first coupon$)$

Question $7$ options:

$1\mathrm{.}012$

$1\mathrm{.}038$

$1\mathrm{.}017$

$1\mathrm{.}015$