Consider two bonds: both pay semiannual interest. Bond $x$ has a coupon of $7\%$ per year, maturity of $20$ years, $y$ ield to maturity of $8\%$ per year, and a face value of $$1,000.$ Bond $Y$ has a coupon of $7\%$ per year, maturity of $20$ years, yield to maturity of $8,5\%$ per year, and a face value of $$1,000.$

Calculate the value of swap out of Bond X into Bond Y $.$

a$.0\mathrm{.}81$ w

b$.4\mathrm{.}12$ w

c$.0\mathrm{.}52$ w

d$.1\mathrm{.}94\%$

e$.3\mathrm{.}76$ W