Show in Excel: Suppose a bank has the following balance sheet:

a$)$ If interest rates decrease for both assets and liabilities by $2\%,$ what is the cumulative impact

on net$-$income after $1$ year, $5$ years, $10$ years and $15$ years? $(10$ points$)$

b$)$ If interest rates decrease for assets by $2\%$ and decrease for liabilities by $3\%,$ what is the

cumulative impact on net$-$income after $1$ year, $5$ years, $10$ years and $15$ years? $(11$ points$)$

$(17$ points total$)$ Suppose you own $$100$ par of a $20-$year bond that pays annually a coupon of

$4\%.$ The market interest rate, $R,$ is $5\mathrm{.}0\%$

a$)$ Calculate the PV$,$ Macauley Duration and Modified Duration $(9$ points$)$

b$)$ Suppose the market interest rate decreases by $1\%.$ Calculate $\frac{P}{P}$ and $P(8$ points$)$

Note: you must build a table and not use Excel bond or interest rate functions.