You have just completed your MBA and accepted a position with a financial consulting company. Among other responsibilities, you have been assigned to one of the company$$s clients, Emma Golding, who needs some financial planning advice. Emma is recently widowed and just received a tax$-$free life insurance payment of $$100,000.$ Emma also has $$245,000$ tucked away in a savings account. She has three main goals in mind. First, she wants to provide for her only child$$s college education. The child will attend college in $4$ years from today and will require tuition payments twice per year over each of the child$$s four years in college. The payments must be made at the beginning of the year and midway through each year. The first year$$s semi$-$annual payments are each $$10,000,$ the second year$$s semi$-$annual payments are each $$11,000,$ the third year$$s semi$-$annual payments are each $$12,000,$ and the fourth year$$s semi$-$annual payments are each $$13,000.$ Emma$$s second goal is to purchase a classic $1960$s vintage automobile which will cost $$92,000$ and be paid for in full immediately. Her third goal is to retire in $15$ years from now and draw $$6,000$ each month over her planned retirement over the following $15$ years. These funds will need to be available at the beginning of each month. Under the assumption Emma can make annual end of year deposits into an account offering a $4\mathrm{.}5$ percent rate of return after taxes before and during retirement, how much would those deposits have to be in order to achieve her financial objectives? Clearly show your work.