Consider a U$.$S$.$ Treasury note with two years to maturity. The coupon rate is $4\%$ and

coupons are paid annually.

$($a$)$ The bond is issued at par. What is duration?

$($b$)$ One year later, the interest rate has decreased to $3\%.$ What is duration at this time?

$($c$)$ How large is the capital gain or loss over the first year of the life of the bond?