Question

1. In 2020, Dr. Chen’s daughter is 7-year old, and Dr. Chen is planning for his daughter’s college fund. He expects his daughter to start her college education at the age of 18, which is 11 years from now. The expected cost of tuition only for a 4-year college education in 2032 is $94,800 at a public, in-state university. The college fund is invested to gain investment returns. Dr. Chen is considering two investment options. The first is a mutual fund that is expected to provide an annual return of 7%. The second is a bank deposit account that offers an annual return of 3%. Dr. Chen decides to put a fixed amount of money every month into the college fund starting from January 2020 to January 2032 (12 months × 11 years). The interest is monthly compounded.

1. Between mutual fund and bank deposit, which investment option is the better one if maximizing the interests is the priority, and why? If Dr. Chen prefers an investment with less risk, which one should he choose?
2. With the better investment option, if Dr. Chen starts saving in January 2020, how much money does he need to put in every month to fully cover his daughter’s college tuition if he wants the account fully funded when she turns 18? (Hint: There are 11 full years left for Dr. Chen to save for his daughter. We assume Dr. Chen’s daughter will do a four-year college with a fixed annual tuition of $94,800 per year.)

Answer 1

(a) If Maximising returns is the priority, it is better to invest in Mutual funds, as it is giving higher interest when compared to bank deposits.

However, if Dr.Chen chooses to invest in less risk, he should choose investing in bank deposit instead of mutual funds, as mutual funds arfe subject market risks.

(b)

a	Mutual Fund
	Annual Tution Cost	n	i	1+i	(1+i)^-n	1- [(1+i)^-n]	PVAF = [1- [(1+r)^-n]] /r	Amount required at age 18
	$        94,800	4	7.00%	1.0700	0.7629	0.2371	3.3872	$                                321,108
	Amount required at age 18	n = 12 Mts *11 yrs	r = (7/12)%	1+r	(1+r)^n	[(1+r)^n] - 1	[(1+r)^n] - 1/r	{ [(1+r)^n] - 1/r}(1+i)	Saving Required per Month
	$     321,108	132	0.5833%	1.00583	2.1549	1.1549	197.990	199.1446474	$         1,612.43
b	Fixed Deposit
	Annual Tution Cost	n	i	1+i	(1+i)^-n	1- [(1+i)^-n]	PVAF = [1- [(1+r)^-n]] /r	Amount required at age 18
	$        94,800	4	3.00%	1.0300	0.8885	0.1115	3.7171	$                                352,381
	Amount required at age 18	n = 12 Mts *11 yrs	r = (3/12)%	1+r	(1+r)^n	[(1+r)^n] - 1	[(1+r)^n] - 1/r	{ [(1+r)^n] - 1/r}(1+i)	Saving Required per Month
	$     352,381	132	0.2500%	1.00250	1.3904	0.3904	156.158	156.548566	$               2,257