financial markets and instrument valuation

Consider a portfolio made up of the following assets: - An annuity due in 10 years that pays $100 each year, with a rate of 6% effective per year. - A perpetuity that pays $50 each year - not valued at an effective annual rate of 5.5% - A 5-year bond with a coupon rate of 8% semi-annual nominal, face value equal to the redemption value of $1,000 and with a rate of return of 7% nominal semi-annual Questions: a) Calculate the price, duration and modified duration of each of the assets. b) Calculate the total value, duration, and modified duration of the portfolio. c) Approximate the value of the portfolio if the rates of the assets that comprise it fall 50 points bases. d) Approximate the value of the portfolio if the bond rate rises by 25 basis points, the interest rate. e) annuity drops 10 basis points, and the perpetuity rate remains constant