Question

Ken and Amy Charvet have two children, ages 4 and 6. The Charvets want to start saving for their children’s education. Each child will spend 5 years at college and will begin at age 18. College currently costs $30,000 per year and is expected to increase at 7% per year. Assuming the Charvets can earn an annual compound investment return of 12% and inflation is 4%, how much must the Charvets deposit at the end of each year to pay for their children’s educational requirements until the younger child goes to school? Assume that education expenses are withdrawn at the beginning of each year and that the last deposit will be made at the beginning of the first year of the younger child.

Answer 1

step 1: Calculation of value of total amount required for college expenses 14 years from now (i.e. till the date of last deposit):

• The elder child will start college 12 years from now and attend it for next 5 years:

Year	College fee payment for elder child (increased @ 7%p.a. and inflation effect @4%)	Future value factor @ 7.52% [((1+0.12)*(1-0.04))-1]	Value of fees at T=14
12	=30000*(1.07^12)*(1.04^12) = 108174.94	=(1.0752^2) = 1.1561	125,056.18
13	=30000*(1.07^13)*(1.04^13) = 120377.07	=(1.0752^1) = 1.0752	129,429.43
		TOTAL	254,485.61

Year	College fee payment for elder child (increased @ 7%p.a. and inflation effect @4%)	Present value factor @ 7.52% [((1+0.12)*(1-0.04))-1]	Value of fees at T=14
14	=30000*(1.07^14)*(1.04^14) = 133955.61	=1/(1.0752^0) = 1.0000	133,955.61
15	=30000*(1.07^15)*(1.04^15) = 149065.8	=1/(1.0752^1) = 0.9301	138,640.07
16	=30000*(1.07^16)*(1.04^16) = 165880.42	=1/(1.0752^2) = 0.8650	143,488.34
		TOTAL	416,084.01

• The younger child will start college 14 years from now and attend it for next 5 years:

Year	College fee payment for elder child (increased @ 7%p.a. and inflation effect @4%)	Present value factor @ 7.52% [((1+0.12)*(1-0.04))-1]	Value of fees at T=14
14	=30000*(1.07^14)*(1.04^14) = 133955.61	=1/(1.0752^0) = 1.0000	133,955.61
15	=30000*(1.07^15)*(1.04^15) = 149065.8	=1/(1.0752^1) = 0.9301	138,640.07
16	=30000*(1.07^16)*(1.04^16) = 165880.42	=1/(1.0752^2) = 0.8650	143,488.34
17	=30000*(1.07^17)*(1.04^17) = 184591.73	=1/(1.0752^3) = 0.8045	148,506.16
18	=30000*(1.07^18)*(1.04^18) = 205413.68	=1/(1.0752^4) = 0.7482	153,699.46
		TOTAL	718,289.63

Total amount required at the beginning of year 14= 254,485.61+416084.01+718289.63 = 1,388,859.26

Step 2:Calculation of yearly contributions required

Using financial calculator in END mode: N=14, I/Y = 7.52%, PV=0, FV= -1,388,859.26, CPT--->PMT = 59,439.53 per annum, which is the payment to be made.