A bank loan of $250,525 at 6.6% interest compounded monthly is made in order to buy a house and is paid off at the rate of $1600 per month for 30 years. The balance at any time is the amount still owed on the loan–that is, the amount that would have to be paid out to repay the loan all at once at that time. 

(a) Give the difference equation for y , n the balance after n months. 

(b) Express in mathematical notation the fact that the loan is paid off after 30 years.