Company A desires a variable$-$rate loan but currently has a better deal from the fixed$-$rate market at a rate of $\mathrm{.}13.$ If Company A borrows from the variable$-$rate market, the cost would be LIBOR$+\mathrm{.}02.$ In contrast, Company B$,$ which prefers a fixed$-$rate loan, has a better deal from the variable$-$rate market at LIBOR$+\mathrm{.}03.$ If Company B borrows from the fixed$-$rate market, the cost would be $\mathrm{.}16.$ Knowing both companies' needs, Bank C designed a swap deal. The deal is outlined in the following:

Company A obtains a fixed$-$rate loan at $.13.$

Company B obtains a variable$-$rate loan at LIBOR$+.03.$

Company A pays Bank $C$ a variable rate of LIBOR$+.01$ and receives a fixed rate of $\mathrm{.}133$ from the bank.

Company B pays Bank $C$ a fixed rate of $\mathrm{.}145$ and receives a variable rate of LIBOR$+.02$ from the bank.

How much is the cost saving to Company $B$ and how much is the total gain to the bank?

Select one:

a$.$ Cost savings for $B$:$0\mathrm{.}5\%,$ and the gain for bank: $0\mathrm{.}2\%$

b$.$ Cost savings for $B$:$0\mathrm{.}7\%,$ and the gain for bank: $0\mathrm{.}2\%$

c$.$ Cost savings for $B$:$0\mathrm{.}4\%,$ and the gain for bank: $0\mathrm{.}4\%$

d$.$ Cost savings for $B$:$1\%,$ and the gain for bank: $0\mathrm{.}3\%$

e$.$ Cost savings for $B$:$0\mathrm{.}6\%,$ and the gain for bank: $0\mathrm{.}3\%$