$1.$ Consider a $50$m swap that has a remaining life of $10$ months. The terms of the swap require the $6-$month LIBOR to be exchanged for $8\%$ per annum with semi$-$annual compounding. The current swap rate being exchanged for LIBOR in swaps of all maturities is $6\%$ per annum with continuous compounding. Two months ago the $6-$month LIBOR was $5\mathrm{.}4\%$ per annum. Calculate the value of the swap to the party paying floating.