Company A wants to invest funds at a floating rate and Company B wants to invest funds at a fixed rate. Company A can invest at a fixed rate of $6\%$ or a floating rate of LIBOR$+1\%.$ Company B can invest at a fixed rate of $7\%$ or a floating rate of LIBOR$+3\%.$ Design an interest rate swap that benefits both companies equally and gives a bank, as intermediary, $20$ bps per year. Under the terms of the swap, what interest rate will Company A pay to the bank?

A$.$

$3\mathrm{.}4\%$

B$.$

$3\mathrm{.}6\%$

C$.$

$4\mathrm{.}4\%$

D$.$

$4\mathrm{.}6\%$

E$.$

LIBOR