Show work and formulas used. No excel. Thank you.

t rates is flat est aturity is anyb,onfe o It is assumed that the term structure of interest rates is a. that the yield on a zero coupon bond with any time to m j> 0 per year. An investor owns a portfolio of two bonds, O which has present value 50,000 and Macaulay duration 8 y and the other has present value 30,000 and Macaulay duration years one of The investor would like to rebalance the portfolio so that the Macaulay duration of the portfolio becomes 7 years. The rebalancing will be done by selling some of one of the bonds to decrease the holding of that bond and using the proceeds to buy more of the other bond to increase its holding. The total value of the portfolio will still be 80,000 after rebalancing. Which of the following is the correct action to rebalance the portfolio? (a) No action is needed since the portfolio already has a duration (b) Sell 20,000 of the 6-year duration bond and buy 20,000 of (c) Sell 10,000 of the 6-year duration bond and buy 10,000 of (d) Sell 20,000 of the 8-year duration bond and buy 20,000 o (e) Sell 10,000 of the 8-year duration bond and buy 10,000 of of 7 years. the 8-year duration bond. the 8-year duration bond. the 6-year duration bond. the 6-year duration bond. It is assumed that the term structure of interest rnto