Assume the zero$-$coupon yields on default$-$free securities are as summarized in the following table: $($Click on the following icon

What is the price today of a two$-$year, default$-$free security with a face value of $$1,000$ and an annual coupon rate of $3\%?$ Does this bond trade at a discount, at par, or at a premium?

Note: Assume annual compounding.

b$.$ If the yield to maturity of the bond rises to $1\mathrm{.}36\%($APR with semiannual compounding$),$ at what price will the bond trade?