b$)$ a$.$ What is the duration of a two$-$year bond that pays an annual coupon of $10$ percent and has a current yield to maturity of $12$ percent? Use $$1,000$ as the face value.

b$.$ What is the duration of a two$-$year zero$-$coupon bond that is yielding $11\mathrm{.}5$ percent? Use $$1,000$ as the face value.

c$.$ Given these answers, how does duration differ from maturity?

$D=\frac{{\displaystyle \underset{t=1}{\overset{N}{}}}\frac{C{F}_{t}t}{(1+r{)}^t}}{{\displaystyle \underset{t=1}{\overset{N}{}}}\frac{C{F}_t}{(1+r{)}^t}}=\frac{{\displaystyle \underset{t=1}{\overset{N}{}}}P{V}_{t}t}{{\displaystyle \underset{t=1}{\overset{N}{}}}P{V}_t}$