John and Michael pay $6,780.31 for a portfolio consisting of a 2-year Zero Coupon Bond with maturity value of $5,000 and a 3-year Zero Coupon Bond with maturity value of $4,000.

a.Using Newton's Method with a table of several rows, find the yield to maturity per annum compounded semiannually. Your final answer should be correct to 3 places after the decimal point. (Check your answer by inserting it into the original equation.)

b.Using the definition of Macaulay Duration and the result from part a, find the Macaulay Duration of the portfolio. You final answer should be stated in years and should be correct to 3 places after the decimal point.

c.Using the results from part a and part b and assuming that the reinvestment rate equals the yield to maturity, find the terminal wealth of the portfolio at the Macaulay Duration time. Your final answer should be correct to 3 places after the decimal point.

d.Using differential calculus and the result from part a, find the dollar convexity and the convexity of the portfolio. Your final answer for the convexity should be correct to 3 places after the decimal point and stated as per annum (years).

e.If yields decrease by 50 basis points per annum compounded semiannually then using the results of parts a, b, and d and Taylor's Theorem find the predicted approximate new price of the portfolio. Your final answer should be correct to 3 places after the decimal point. (Compare your answer to the result of inserting the new yield into the original equation. They should be close.)