Q$10.$ Suppose the spot and six$-$month forward rates on the Norwegian krone are $Kr8\mathrm{.}39$ and $Kr8\mathrm{.}48,$ respectively. The annual risk$-$free rate in the United States is $3\mathrm{.}8$ percent, and the annual risk$-$free rate in Norway is $5\mathrm{.}7$ percent.

a$.$ Is there an arbitrage opportunity here? If so$,$ how would you exploit it$?$

b$.$ What must the six$-$month forward rate be to prevent arbitrage?