The US treasury has two bonds outstanding, both with $2\mathrm{.}0\%$ coupon rate. The first has one

year to maturity, the second $20$ years to maturity. Assume semi$-$annual coupon payment, and

$3\mathrm{.}0\%$ yield.

a$.$ Calculate the two bonds prices.

b$.$ Market conditions have changed, and the bonds yield has dropped to $2\mathrm{.}6\%.$ Price both US

treasury bonds and evaluate the each bond capital gain rate. What can you conclude about the

relative loss and the bonds maturity?