The cost of a home you want to purchase is $$200,000.$ To qualify for a mortgage, your lender wants

a $10\%$ down payment. Your mortgage interest rate is $3\%$ for $30$ years and you have to pay three points.

a$.$ How much money do you need for the down payment? $(4$ points$)$

b$.$ How much will your mortgage be$?(3$ points$)$

c$.$ How much will you have to pay for the points? $(4$ points$)$

d$.$ What will your monthly mortgage payment be$?(10$ points$)$

e$.$ By the end of the loan, what will be the total of all your payments. $(5$ points$)$