Problem $4\mathrm{.}15.$ Assuming that SOFR rates are as below, what is the value of an FRA where the holder will pay SOFR and receive $\backslash (4\mathrm{.}5\backslash \%\backslash )($quarterly compounded$)$ for a three$-$month period starting in one year on a principal of $\backslash (\backslash$$ $1,000,000\backslash )?$ Problem $7\mathrm{.}2.$ A $\backslash (\backslash$$ $100\backslash )$ million interest rate swap has a remaining life of $10$ months. Under the terms of the swap, six$-$month LIBOR is exchanged for $\backslash (4\backslash \%\backslash )$ per annum $($compounded semiannually$).$ Six$-$month LIBOR forward rates for all maturities are $\backslash (3\backslash \%\backslash )($with semiannual compounding$).$ The six$-$month LIBOR rate was $\backslash (2\mathrm{.}4\backslash \%\backslash )$ two months ago. OIS rates for all maturities are $\backslash (2\mathrm{.}7\backslash \%\backslash )$ with continuous compounding. What is the current value of the swap to the party paying floating? What is the value to the party paying fixed?