$2.$ What is the effect on a bond's duration of increasing the bond's maturity? As in the previ$-$

ous example, use a numerical example and plot the answer. Note that as $N,$ the bond

becomes a consol $($a bond that has no repayment of principal but an infinite stream of

coupon payments$).$ The duration of a consol is given by $\frac{1+YTM}{YTM}.$ Show that your

numerical answers converge to this formula.

$3.$ "Duration can be viewed as a proxy for the riskiness of a bond. All other things being

equal, the riskier of two bonds should have lower duration." Check this claim with an

example. What is its economic logic?

$4.$ A pure discount bond with maturity $N$ is a bond with no payments at times $t=1,$dots,$N-1$;

at time $t=N,$ a pure discount bond has a single terminal payment of both principal and

interest. What is the duration of such a bond?

These $3$ questions please help. The table is used for questions