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 $$12,000$ 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.

$$7,570\mathrm{.}97$

$$9,253\mathrm{.}40$

$$10,935\mathrm{.}84$

$$8,412\mathrm{.}18$

$$10,094\mathrm{.}62$