Problem 1: Billys College Fund

1) Jane Smith wants to send her son Billy to college. Billy just turned 3 years-old today, September 1st, and Jane expects Billy to enter college exactly 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.

a) 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 paid in tuition costs when Billy graduates from college? Round your final answer to the nearest dollar.

b) 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 dollar 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 annual tuition payments.

What is the monthly periodic interest rate that corresponds to an 8% EAR? (provide your answer with 4 decimals)

c) If she makes her first investment in Bills college savings account at the end of this month, what is the fixed dollar amount (round the amount to 2 decimals) that she must invest each month in order to pay for Billys college? (Remember that this savings account requires her to make the same dollar investment each month, starting from the end of this month until the beginning day, September 1st, of his last academic year of college.)