MLK Bank has an asset portfolio that consists of $$100$ million of $30-$year, $8$ percent annual coupon, $$1,000$ bonds that sell at par.

a$.$ What will be the bonds' new prices if market yields change immediately by $+-0\mathrm{.}10$ percent? What will be the new prices if market yields change immediately by $+-2\mathrm{.}00$ percent?

b$.$ The duration of these bonds is $12\mathrm{.}1608$ years. What are the predicted bond prices in each of the four cases using the duration rule? What is the amount of error between the duration prediction and the actual market values?