Please explain in detail both answers.

$1.$ You want to purchase a house: your maximum monthly payment is $$2,800,$ and you also have a saving of $$125,000$ as the down payment. You apply for a $30-$year fixed mortgage loan with APR $5\mathrm{.}99\%.$ What is the maximum house price you can afford to buy?

$2.$ Professor$$s Annuity Corp. offers a lifetime annuity to retiring professors. For a payment of $$350,000$ at age $65,$ the firm will pay the retiring professor $$2,800$ a month until death. If the professor$$s remaining life expectancy is $30$ years, what is the monthly rate on this annuity? What is the effective annual rate?