Joe and June Green are planning for their children's college education. Joe would like his kids to attend his alma mater where tuition is currently $20,000 per year. Tuition costs are expected to increase by 4% each year. Their son, David, just turned 2 years old today, September 1, 2015. David is expected to begin college the year in which he turns 18 years old and each will complete his schooling in four years. College tuition must be paid at the beginning of each school year on August 31.

Grandma Green invested $5,000 in a mutual fund the day David was born. The mutual fund investment has earned and is expected to continue to earn 8% per year. Joe and June will now begin adding to this fund every August 31st (beginning with August 31, 2016) to ensure that there is enough money to send David to college.

(a) How much money must Joe and June put into the college fund each of the next 15 years if their goal is to have enough money in the investment account by the time David begins college?

(b) Joe is worried that he and June cannot afford to contribute to the college fund right away. He suggests waiting a few years before making the equal annual contributions. If Joe and June begin making deposits on August 31, 2019, rather than August 31, 2016, how much higher with their annual deposits have to be?

(c) If the mutual fund earns 7.8% compounded quarterly, will the amount required in part (a) be higher or lower? Support your answer.