Suppose a bank has financed a $$11,000,00010-$year loan with an annual coupon rate of $8\mathrm{.}34\%$ witha $15-$year $$11,000,000$ bond with a semiannual coupon rate of $6\mathrm{.}76\%.$ The yield on the loan is $8\mathrm{.}55\%$and the yield on the bond is $6\mathrm{.}32\%.$

a$.$ Calculate the $($i$)$ duration and $($ii$)$ modified duration for the loan.

b$.$ Calculate the $($i$)$ duration and $($ii$)$ modified duration for the bond.

c$.$ If market interest rates decrease $150$ basis points, estimate the effect on the market value of thebank$$s equity from this arrangement.