Find the price of a $2-$year default$-$free security with a face value of $$1000$ and an annual coupon rate of $4\%$ based on the zero$-$coupon yields on default$-$free securities provided below:

Maturity Zero$-$Coupon Yields

$1$ year $0\mathrm{.}040$

$2$ years $0\mathrm{.}055$

$3$ years $0\mathrm{.}064$

$4$ years $0\mathrm{.}068$