Bond relationships. You manage a bond portfolio with two bonds. The information for each bond is providest in the table below:

$\backslash$table$[[,$Bond I,Bond $2,$Portfolio$],[$Maturity$,7$ years,$12$ years,$],[$Coupon$,4\mathrm{.}00\%,6\mathrm{.}00\%,],[$Yield to Maturity,$4\mathrm{.}40\%,7\mathrm{.}60\%,],[$Duration$,6\mathrm{.}1619,8\mathrm{.}4631,],[$Value$,$$$195,225,$$$262,646,5457,871]]$

a$.$ Calculate the modified duration for Bond $1.$

b$.$ Calculate the modificd duration for Bond $2.$

Assume yields decrease by $30$ basis points.

c$.$ Using the modified duration $("$a$"),$ calculate the approximate new value of Bond I.

d$.$ Using the modified duration $("$b$"),$ calculate the approximate new value of Bond $2.$

e$.$ Using a modified duration of $7\mathrm{.}2476$ for the portfolio, calculate the approximate new value of the portfolio.