Consider the following two banks:

a$.$ Bank $1$ has assets composed solely of a $10-$year, $12$ percent coupon, $$1$ million loan with a $12$ percent yield to maturity. It is financed with a $10-$year, $10$ percent coupon, $$1$ million CD with a $10$ percent yield to maturity.

b$.$ Bank $2$ has assets composed solely of a $7-$year, $12$ percent, zero$-$coupon bond with a current value of $$894,006\mathrm{.}20$ and a maturity value of $$1,976,362\mathrm{.}88.$ It is financed with a $10-$year, $8\mathrm{.}275$ percent coupon, $$1,000,000$ face value CD with a yield to maturity of $10$ percent.

c$.$ All securities except the zero$-$coupon bond pay interest annually.

a$.$ If interest rates rise by $1$ percent $(100$ basis points$),$ how do the values of the assets and liabilities of each bank change?

b$.$ What accounts for the differences between the two banks' accounts? Why did assets and liabilities diverge more for Bank $1$ Relative to Bank $2$