Amrita has just arranged to purchase a $$1,000,000$ vacation home in the Manali with a $10$ percent down payment. The mortgage has a $6$ percent APR, compounded monthly, and calls for equal monthly payments over the next $30$ years. Her first payment will be due one month from now. $$

a$.$ What is the amount of monthly installment she will need to pay?

b$.$ After five years if she decides to repay her loan and there is a $1\%$ penalty on the prepaid amount, what will be her total cash outflow at that point in time?