One client deposit $10, 000 into a bank at the rate of 2% and the bank lends the money to another client at the rate of 6%, both for one year. The deposit will be paid back to the client at the end of the year. The loan is actually repaid with the same amount at each month end. The rates are both compounded continuously per annum.

(a) If the bank does not use loan repayments to invest, how much will the bank have in one year?

(b) If the bank invests loan repayments with the return rate 3% per annum with monthly compounding, then how much will the bank have in one year?