MLK Bank has an asset portfolio that consists of $$160$ million of $15-$year, $8\mathrm{.}5$ percent annual coupon, $$1,000$ bonds that sell at par.

a$-1.$ What will be the bonds$$ new prices if market yields change immediately by $\backslash$pm $0\mathrm{.}10$ percent?

a$-2.$ What will be the new prices if market yields change immediately by $\backslash$pm $2\mathrm{.}00$ percent?

b$-1.$ The duration of these bonds is $9\mathrm{.}0101$ years. What are the predicted bond prices in each of the four cases using the duration rule?

b$-2.$ What is the amount of error between the duration prediction and the actual market values?