$11-13.$ A group of private investors borrowed $$30$ million to build $300$ new luxury apartments near a large university. The money was borrowed at $6\%$ annual interest, and the loan is to be repaid in equal annual amounts over a $40-$year period. Annual operating, maintenance, and insurance expenses are estimated to be $$4,000$ per apartment. This expense will be incurred even if an apartment is vacant. The rental fee for each apartment will be $$12,000$ per year, and the worst$-$case occupancy rate is projected to be $80\%.$ Investigate the sensitivity of annual profit $($or loss$)$ to $($a$)$ changes in the occupancy rate and $($b$)$ changes in the annual rental fee. $(11\mathrm{.}3)$