Morgan wants to buy a $10-$year, AAA$-$rated, $$1,000$ par value, zero$-$coupon bond being sold by Upsize Industries, Inc. The yield to maturity on similar bonds is estimated to be $4\mathrm{.}6\%.$ How much would he have to pay for the bond $($interest is compounded semiannually$)?$

$$634\mathrm{.}58$

$$637\mathrm{.}80$

$$535\mathrm{.}43$

$$1,000\mathrm{.}00$