a$.)$ I am looking to invest in an apartment building. The building has annual rents of $$50,000,$ and I think I can sell the building in $10$ years for $$500,000.$ If I need a $12\%$ rate of return, what is the most I should pay for the building?

b$.)$ Same apartment building. I can buy the building for $$600,000.$ What do I have to sell the building for in $10$ years to get my $12\%$ out of the investment?