$1.$ A bond has a Macaulay duration of $10.$ The yield is $5\%.$ What is the modified duration? If the bond is priced at $100$ and rates decrease $50$ bps$,$ what is the bond price? Walk me through the steps.

Note: In making this calculation, we ignored "convexity". What is convexity and would convexity make the final price higher or lower than your answer above?

$2.$ A borrower comes to market with a $2\%$ yield for a $10-$year bond. The DV$01$ is $9(0\mathrm{.}0009).$

An investor comes in with a strong preference for a discount bond. The issuer finds that attractive.

For technical reasons, the bond must have a price of at least $90\%.$ So they agree to issue a bond at $90\%.$

What would the coupon be$?$ How did you calculate that? Explain the logic. Please show work.

$3.$ Build out a model to calculate the duration of a $5$ year bond with annual payments. Allow the user to input the coupon and yield. Model should calculate a bond price and a duration.

Use this model to calculate a duration for a $5\%$ coupon and $5\%$ yield. Now recalculate duration at $4\%.$ Calculate convexity $($choose some scenario and show me the convexity calculation$).$

$4.$ Describe for me the difference between DV$01$ and modified duration.

$5.$ Write one thing you learned from the Mauboussin Investment Committee writeup.