A firm can issue one of the listed products and convert them into the floating rate using IR swaps $($LIBOR for $3\mathrm{.}7\%$ fixed$).$ What is the lowest floating rate that the firm can get?

Fixed rate note: $4\%$

Simple FRN: L $+0\mathrm{.}5\%$

Inverse floater: $7\mathrm{.}6\%-$ L

$($e$.$g$.,$ if we can pay only L $+0\mathrm{.}1\%$ that would be great, but can we obtain such a low rate?$)$

Options:

a$)$ L $+0\mathrm{.}1\%$

b$)$ L $+0\mathrm{.}2\%$

c$)$ L $+0\mathrm{.}3\%$

d$)$ L $+0\mathrm{.}5\%$

Please show all work!