The bank has $$100$ of $3-$months deposits

paying $3\%$ annual interest rate, and $$12$ of

equity. It lends $$100$ for one year at the

$5\%$ interest rate. Deposits are renewable

and interests on loans and deposits are

payable at the end of each quarter.

a$)$ Compute the net interest margin, the

value of loans, deposits and equity at

the end of the year.

b$)$ What happens to the net interest

margin if at the end of the first

quarter market interest rate increases

by $1\%?$ What the bank should do$?$