We have a 7%, 40 year bond. We buy it now at which point market yields are 7%. Interest rates rise substantially to 12% per annum.

a. Derive the price alteration by using duration.

b. Also, find the exact price. Compare the two cases.

c. What strategies will enable us to attain a higher rate of return and protect the value of the portfolio more?

Please answer all the questions and show all the work. Thanks!