Jane Smith wants to send her son Billy to college. Billy just turned 3 years-old today, September 1st, and should enter college on his 18th birthday. After doing some research, Jane finds out that the tuition cost today for a year of study in a good university in the US is about $50,000 payable at the beginning of the academic year (September 1st of each academic year). It takes, on average, 4 years to obtain a bachelors degree. In addition, college costs typically increase by 5% per year.

1. How much will Jane have to pay in total for Billys college education? In other words, what is the total amount of dollars that Jane will have to pay in tuition costs for Billys college degree? Round your final answer to the nearest dollar.

2. Jane opens a college savings account on Billys 3rd birthday, which promises her an effective annual rate of return (EAR) of 8%. This account, which works like an ordinary annuity, requires her to invest the same fixed amount at the end of each month, until the beginning of Billys last academic year, when she is expected to make the last of her 4 tuition payments.

   What is the monthly periodic interest rate that corresponds to an 8% EAR? (Please give your answer as a percentage, with 4 decimal points)

3. If she makes her first investment in this account at the end of this month, what is the minimum amount that she must invest each month to pay for Billys college?

4. Verify your result in question c) by showing that there will always be enough money in the fund to make all four tuition payments and that there will be exactly $0 left in the fund once she has made the fourth and last tuition payment. Remember the main constraints in this investment scheme: - She will invest the same dollar amount each month, starting from the end of this month until the last (4th) tuition payment is made. - The 4 tuition payments are to be made at the beginning of each academic year. Each of these 4 amounts will be taken out of Janes fund when they are due.