$5.(15$ points$)$ A WSJ article on $12/28/2015$ urged millennials to ditch their parents$$ homes and buy their own homes now. $1$ It argues: $$if$,$ for instance, $30-$year mortgage rates rise by one percentage point a year from now and home prices rise by another $5\%,$ a monthly mortgage payment could jump by around $18\%.$ Let$$s verify this statement. Assume the house price is $$500,000$ and the $30-$year mortgage rate is $4\%($APR$)$ at the end of $2015.($i$)(5$ points$)$ What$$s the monthly mortgage payment? $($ii$)(5$ points$)$ If you defer the purchase to the end of $2016,$ what$$s the new monthly mortgage payment $($when the house price increases by $5\%$ and the $30-$year mortgage rate becomes $5\%)?($iii$)(5$ points$)$ Is the statement correct?