The following information is relevant for all sections of this question. Please note this information down, and clearly note down your own workings in case you need to refer back to it in a later section of this question. You own a bond with a face value of $$1,000,$ a coupon rate of $5\%$ and a yield to maturity of $7\%.$ The bond matures in exactly $4$ years.

a$)$ Is the bond a premium or discount bond? Show this without calculating the bond price

B$)$ what is the current price of the bond?

C$)$ what is the duration of the bond? Hint : you can paste your working from an excel file

D$)$ how do you immunise a liability with a duration of part c with the following two bonds : bond A$-10$ year zero coupon bond bond B$-3$ year zero coupon bond?

E$)$ hoe could convexity have an impact on the immunisation strategy in part d$)$ explain.