Question

Part One

1. [Time Value of Money] David, aged 30, wishes to accumulate a college fund for his newborn baby (age 0). Assuming that his baby will need 20,000 each year for four years starting the beginning of his age 18 for college, how much money he needs to put aside right now? If David does not have that amount of money right now, but he can save certain amount of money at the end of each year, how much money each year he needs to save in order to have enough for his son’s college? The annual interest rate is 4%.

Part Two

2. [Time Value of Money] Assume David (from question 1) can invest in a high return fund with expected return 10% each year. Compared to the safe return of 4% in question 2, how much money each year he needs to save now with the high return? (Bonus 5 points): Do you think David should go with the high return option? Why and why not?

Answer 1

Present value of college fund at the newborn's 18^th birthday = Fees in year 18 + Fees in year 19 / (1 + interest rate)¹ + Fees in year 20 / (1 + interest rate)² + Fees in year 21 / (1 + interest rate)³

Present value of college fund at the newborn's 18^th birthday = 20,000 + 20,000 / (1 + 4%)¹ + 20,000 / (1 + 4%)² + 20,000 / (1 + 4%)³

Present value of college fund at the newborn's 18^th birthday = 75,501.82

Present value of college fund today = Present value of college fund at the newborn's 18^th birthday / (1 + interest rate)¹⁸

Present value of college fund today = 75,501.82 / (1 + 4%)¹⁸

Present value of college fund today = 37,269.82

Money he needed to put aside right now = Present value of college fund today = 37,269.82

Yearly installment needed for the college fund = interest rate / ((1 + interest rate)^{no of periods} -1) * Present value of college fund at the newborn's 18^th birthday

Yearly installment needed for the college fund = 4% / ((1 + 4%)¹⁸ -1) * 75,501.82

Yearly installment needed for the college fund = 2944.07

2)

Present value of college fund at the newborn's 18^th birthday = Fees in year 18 + Fees in year 19 / (1 + interest rate)¹ + Fees in year 20 / (1 + interest rate)² + Fees in year 21 / (1 + interest rate)³

Present value of college fund at the newborn's 18^th birthday = 20,000 + 20,000 / (1 + 10%)¹ + 20,000 / (1 + 10%)² + 20,000 / (1 + 10%)³

Present value of college fund at the newborn's 18^th birthday = 69,737.04

Present value of college fund today = Present value of college fund at the newborn's 18^th birthday / (1 + interest rate)¹⁸

Present value of college fund today = 69,737.04 / (1 + 10%)¹⁸

Present value of college fund today = 12,542.82

Money he needed to put aside right now = Present value of college fund today = 12,542.82

Yearly installment needed for the college fund = interest rate / ((1 + interest rate)^{no of periods} -1) * Present value of college fund at the newborn's 18^th birthday

Yearly installment needed for the college fund = 10% / ((1 + 10%)¹⁸ -1) * 69,737.04

Yearly installment needed for the college fund = 1529.35

I feel that David should invest in this high return fund since he has the required time frame & capacity to bear the highly volatile nature of this investment to able to truly earn a 10% annualized return. Th yearly installments also would be smaller.

The only contention for not going for the fund would be at the time of maturity of the fund there could be a drawdown on the fund which will hamper meeting funding requirements.