$(3)$ You are offered the opportunity to put some money away for retirement. You will receive five annual payments of $$25,000$ each beginning in $40$ years. How much would you be willing to invest today if you desire an interest rate of $12\%?$

$(4)$ You are ready to buy a house, and you have $$20,000$ for a down payment and closing costs. Closing costs are estimated to be $4\%$ of the loan value. You have an annual salary of $$36,000,$ and the bank is willing to allow your monthly mortgage payment to be equal to $28\%$ of your monthly income. The interest rate on the loan is $6\%$ per year with monthly compounding per month$)$ for a $30-$year fixed rate loan. How much money will the bank loan you? How much can you offer for the house?