You want to buy a new house with your new salary. The cost of your dream home is $$230,000.$ Luckily you have saved up a down payment of $$14,000$ and can get a loan for the rest at an interest rate of$6\mathrm{.}80\%$ compounded monthly. The loan is for $15$ years plus a one point origination fee and $$3,000$ in closing costs.

a. What is the monthly payment on the loan?

b. What is the effective APR for the loan? $($in $\%)$