Mika wants to buy a condominium. he has the choice of buying it now or renting it with the option to buy at the end of 3 years. if he buys now, he could put $0 down, but he must pay closing costs of $7,100. his monthly mortgage payment will be $675. mika decides to rent instead of buy because it is the cheapest option over the first 3 years. his move-in costs are one month's rent and a $750 security deposit, and he would still need to pay his first month's rent on top of these move-in costs. to the nearest dollar, what is the maximum amount of monthly rent payment he could pay?

The easiest way to conceptualize this, is to think of the total payments he makes by the end of 3 years. If he buys, the calculation is pretty straighforward: he will have to pay 7100$ upfront and have a mortgage payment of 675$ for 3*12=36 months. Suppose now he pays x for rent; His cost will be (x+750$) upfront and then he will also pay 36*x in rent payments. If the rent option is to be better, we have that:
36x+750+x<7100+36*675
37x<7100+36*675-750
37x<30650
x<828$
This is the maximum amount he can pay for rent so that the first 3 years he pays less for the condominium than he would pay if he had bought it.