Hello! If you could please help answer this problem step-by-step and include any formulas used, that would be great! (no excel please) Thank you so much!

2. There is a risk-free bond (let's call it bond Y) that matures 3 years from now with a face value of $200 and a coupon rate of 5% (coupon payments are annual). Its yield to maturity is 6%.

(a) Find the price of the bond.

(b) Find the duration of the bond.

(c) Using the value of duration you just calculated, find by how much the price of the bond will approximately change if the yield to maturity moves (right now) from 6% to 7.5%. (give your answer in percentages)

(d) Assume that you manage a company with liabilities that have a duration of 15 years. Assume that you can invest in a combination of bond Y (this is the bond whose duration you just calculated) and another zero-coupon bond that matures 20 years from now. Which fraction of your assets should you invest in bond Y to immunize your portfolio (by matching exclusively duration, not convexity) against changes in interest rates?

(e) Assume that there exists another bond Z with duration of 4 (this is the duration, not the modified duration) and convexity of 18. Find by how much the price of the bond will approximately change if the yield to maturity moves (right now) from 6% to 7.5%. (give your answer in percentages)