A portfolio consists of three bonds as follows.

$\backslash$table$[[,$Amount Invested,Bond Duration$],[$Bond $x,$$$5,000,8\mathrm{.}6$ years$],[$Bond $Y,$$$4,000,4\mathrm{.}2$ years$],[$Bond Z$,$$$1,000,11\mathrm{.}4$ years$]]$

What is the duration of the bond portfolio?

A$)7\mathrm{.}12$ years

B$)8\mathrm{.}07$ years

C$)8\mathrm{.}69$ years

D$)11\mathrm{.}4$ years

A bond matures in $30$ years, has a $20$ year duration and a yield to maturity of $9\mathrm{.}32\%.$ The change in the level of the market interest rate is $0\mathrm{.}47\%.$ The modified duration is $q,$ and the percentage change in price is $$

A$)9\mathrm{.}4$ years; $-\mathrm{.}47\%$

B$)14.$ years; $4\mathrm{.}7\%$