On a $$1,050,000$ home, on a $30-$ year fixed mortgage, with an interest rate of $5\mathrm{.}29,$ find:

a$.$ The down payment amount $(15\%)$

b$.$ Amount borrowed from bank $($price of home $-$ down payment$)$

c$.$ The monthly payment

d$.$ Total paid back to bank $($principal $+$ interest$)$