The yield to maturity on one$-$year zero$-$coupon Treasury bonds is $2\%$ and the yield to maturity on two$-$year zero$-$coupon Treasury bonds is $2\mathrm{.}5\%?$ The face value of all bonds is $$1,000.$ What is the price and the yield to maturity of the two$-$year Treasury coupon bond that pays $5\%$ in annual coupons?

A$)$ $$1,040\mathrm{.}58$ and $2\mathrm{.}257\%$

B$)$ $$1,035$ and $3\mathrm{.}052\%$

C$)$ $$1,000$ and $5\%$

D$)$ $$1,048\mathrm{.}43$ and $2\mathrm{.}488\%$