Advanced Time Value of Money Problems

(Try to work this question WITHOUT using Excel, get calculationin detail)

Question (College planning)

Your child was just born and you are planning for his/hercollege education. Based on your wonderful experience in FinancialEconomics you decide to send your child to Hofstra University aswell. You anticipate the annual tuition to be $60,000 per year forthe four years of college. You plan on making equal deposits onyour child’s birthday every year starting today, the day of yourchild’s birth. No deposits will be made after starting college. Thefirst tuition payment is due in exactly 18 years from today (theday your child turns 18 – no deposit required, i.e. last deposit ison 17th birthday). Assume the annual expected return on yourinvestments is 10% over this period.

1. (i) Calculate the annual deposit.

2. (ii) Calculate the amount needed if only equal annual depositsare made on birthday’s 5-10 inclusive.

3. (iii) Calculate the amount needed if two equal annual depositsare made on birthday’s 5 and 13.

4. (iv) Answer part (i), now assume tuition rises 10% per year.

5. (v) Answer part (i) assuming first deposit will be made on yourchild’s 1st birthday. All other information is the same. What isthe annual tuition payment? How does it compare to part (i)? Isyour answer surprising?