Consider a $5$ year zero coupon bond issued with a face value of $100$ and a

rate $($yield$)$ of $6\%.$

Compute the value $B$ of this bond

Compute the sensitivities of $B$ to yield and time

Use the first$-$order Taylor expansion to compute the impact on the

value of the bond of a change in yield to $2\%,4\%,8\%,$ and $10\%($do not

consider a change in time$)$

Compute the exact value of the bond for the same changes in yields

and compare your results with the approximations you obtained in the

previous question. Explain why there is a difference.

$*$Repeat the exercise using a second$-$order Taylor expansion and

compare the results