Jim took out a $30$ year, $$200,000$ mortgage on his home with an annual interest rate of $5\mathrm{.}5\%,$ compounded monthly. The following statements are true EXCEPT:

The monthly payments will be: $$1,136$

After the $12$th payment, the total interest payments will be $$10,933$

After the $12$th payment, the total principal payments will be $$2,694$

After the $12$th payment, the mortgage balance will be $$194,360$