A $7$ percent semiannual coupon bond with two years to maturity and a current price of $$1,055\mathrm{.}30.$ Use the YTM and Macaulay Duration from the previous question for the following calculations.

a$).$ What is the modified duration?

b$).$ Suppose the yield on the bond suddenly increases by $2$ percentage points. Use duration to estimate the new price of the bond.

c$).$ What is the new bond price calculated from the usual bond pricing formula?

d$).$ What is the dollar value of an $01$ for the bond?

e$).$ What is the yield value of a $32$nd for this bond?

$($Note: Please round your answer to four decimal places.$)$