Betty and Bob pay $$6,479\mathrm{.}845$ 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. Your 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$).$

Dollar convexity $\_\_\_\_\_\_\_\_\_\_\_\_$ Convexity $\_\_\_\_\_\_\_\_\_\_\_\_\_$

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.$)$ New Price $\_\_\_\_\_\_\_\_\_\_\_$