A $2-$year $$1,000$ par zero$-$coupon bond is currently priced at $$819\mathrm{.}00.$ A $2-$year $$1,000$ annuity is currently priced at $$1,712\mathrm{.}52.$ If you want to invest $$10,000$ in one of the two securities$,$ which is a better buy? You can assume

$(1)$ the pure expectations theory of interest rates holds,

$(2)$ neither bond has any default risk, maturity premium, or liquidity premium, and

$(3)$ you can purchase partial bonds.