A borrowerwishes to take out a $$600,000$ mortgage to purchase an $$800,000$ house. They are quoted a $7\%$ mortgage rate on a $30y$ fixed rate mortgage, paid monthly:

a$.$ What is the LTV of this loan?

b$.$ Assuming the borrower has good credit $($a high FICO, low DII$),$ would this loan be eltighle to be guaranteed by Fannie$/$Freddie$?$ Would it require the borrower to take out mortgage insurance and why$/$hhy not?