The market has the following expectations for $1-$year rates of return for each of the next $5$ years:Year $1=4\mathrm{.}00\%$; Year $2=4\mathrm{.}80\%$; Year $3=5\mathrm{.}60\%$; Year $4=6\mathrm{.}40\%$; Year $5=5\mathrm{.}80\%$In $2$ years, you will buy a U$.$S$.$ Treasury, zero coupon $($discount$)$ security that pays no coupon, but will mature for $$13,000$ in $3$ years $($you will hold the security over years $3,4,$ and $5).$Assuming that the Pure Expectations Theory of the term structure is correct, determine how much you expect to pay for this security when you buy it in two years.$$8,412\mathrm{.}18$$$9,253\mathrm{.}40$$$10,094\mathrm{.}62$ $$7,570\mathrm{.}97$ $$10,935\mathrm{.}84$