Question

Mr. and Mrs. Smith's first child was just born. The expectation is that in 18 years the child will attend college. The current average cost of one year of college is $25,000. College costs are expected to increase by an average of 4% annually over the next 18 years. The Smith's plan on beginning a college savings plan wherein they will invest the same dollar amount, at the end of each year, for the next 18 years. The expectation is that the invested monies will earn an average annual rate of return of 7%. The back-up plan is to reach into their accumulated savings to date and make a one-time investment, today, with the expectation being to earn an average annual rate of return of 7% over the next 18 years.

a. The forecasted cost of the first year of college (in 18 years) for the child is approximately

b.In order to have a college savings investment account balance that reaches $90,000 in 18 years the Smith's will need to save the amount of _____________________ annually for 18 years.

c. In order to have a college savings investment account balance that reaches $90,000 in 18 years the Smith's will need to invest the amount nearest to ____________________ today (one time today).

Answer 1

a

Expected cost = 25,000 * 1.04^25 = 50,645.41

b

Payment required	=	FV*r /[(1+r)^n -1]
Future value	FV	90,000.00
Rate per period	r
Annual interest		7.0%
Number of payments per year		1
Interest rate per period		0.07/1=
Interest rate per period		7.000%
Number of periods	n
Number of years		18
Periods per year		1
number of periods		18
Period payment	=	90000*0.07/ [(1+0.07)^18 -1]
	=	2,647.13

Annual savings is $2647.13

c

Present value of money:	=	FV/ (1+r) ^N
Future value	FV=	$               90,000
Rate of interest	r=	7%
Number of years	N=	18
Present value	=	90000/ (1+0.07)^18
	=	$         26,627.75

Lumpsum payment today is $26,627.75

please rate.