A currency swap has a remaining life of $15$ months. It involves exchanging interest at $9\mathrm{.}7\%$ on $20,000$ for interest at $6\mathrm{.}2\%$ on $$30,000$ once a year. The term structure of risk$-$free interest rates in the United Kingdom is flat at $6\mathrm{.}7\%$ and the term structure of risk$-$free interest rates in the US is flat at $3\mathrm{.}6\%($both with continuous compounding$).$ The current exchange rate $($dollars per pound sterling$)$ is $1\mathrm{.}55.$ What is the value of the swap $($in dollars$)$ to the party paying sterling?