You have decided to invest in a warehouse that is currently being rented out for $$35,000$ per year for the next $5$ years with rent paid at the beginning of each year. After the $5$ year lease expires, you expect to be able to raise the rent by $3\%$ per year with annual payments at the beginning of each year for the next $10$ years. What annual rent will you be earning at the beginning of the $15$th year to the nearest cent? Continue using the data from problem $11.$ If you require an $11\%$ return on your investment for this warehouse, and you plan on selling the warehouse for $$500,000$ at the end of the $15$th year, what is the maximum price that you would be willing to pay for this warehouse today to the nearest cent? Do not enter $ or comma in the answer box. For example, if your answer is $$12,300\mathrm{.}456$ then enter as $12300\mathrm{.}46$ in the answer box.