Mr. and Ms. Gallagher are happily married. They were blessed with a wonderful daughter exactly 10 years ago. Today is Rachels 10^th birthday. She is very clever. Her parents started to plan for the future education of Rachel. She will start college when she is 18. Her college education will last for four years. Mr. and Ms. Gallagher examined and realize that the college education (including all the expenses) will cost $15,000 for the first year today. The inflation rate is 5% and they think that it will stay constant for the next 15 years at that level. The college expenditures are also going to increase with the same inflation rate for each year. The payments for the college have to be paid at the beginning of each year. The first payment will be done when Hermione registered at the age of 18. When they calculated the amount of money they need for the Rachel's education they realized that they have to save some money. Fortunately, at the 15^th birthday Rachels grandparents are planning to give her a check for $15,000. Mr. and Ms. Gallagher decided to use this money for the college education as well. They think that they can set aside a fixed amount of money each month. The first payment will be done today and the last payment will be done when Rachel is 18. The interest rate on those savings accounts is 11.6601% compounding semi-annually.

1. Calculate the amount Mr. and Ms. Gallagher needs for Rachel's education at the beginning of each year in the college.
2. Draw the time line and show all cash flows.
3. Calculate the effective interest rate
4. Compute the amount of monthly payments Mr. and Ms. Gallagher have to make in order to have the enough money for Rachel's college education of four years when she became 18. Please do not forget to take into account the $15,000 check given by the grandparents. Assume the interest rate is constant for the next 20 years