Question

Victor and Jasmine Gonzalez were discussing how to plan for their three young sons’ university education. Stephen turned 12-years old in April, Jack turned 9 in January, and Danny turned 7 in March. Although university was still a long way off for the boys, Victor and Jasmine wanted to ensure enough funds were available for their studies.

Victor and Jasmine decided to provide each son with a monthly allowance that would cover tuition and some living expenses. Because they were uncertain about the boys’ finding summer jobs in the future, Victor and Jasmine decided their sons would receive the allowance at the beginning of each month for four years. The parents also assumed that the costs of education would continue to increase.

Stephen would receive an allowance of $1000 per month starting September 1 of the year he turns 18.

Jack would receive an allowance that is 8% more than Stephen’s allowance. He would also receive it at the beginning of September 1 of the year he turns 18.

Danny would receive an allowance that is 10% more than Jack’s at the beginning of September of the year he turns 18.

Victor and Jasmine visited their local bank manager to fund the investment that would pay for the boys’ allowances for university. The bank manager suggested an investment paying interest of 4.0% compounded monthly, from now until the three boys had each completed their four years of education. Victor and Jasmine thought this sounded reasonable. So on June 1, a week after talking with the bank manager, they deposited the sum of money necessary to finance their sons’ post-secondary educations.

Questions
a. How much allowance will each of the boys receive per month based on their parents’ assumptions of price increases?
b. (i) How much money must Victor and Jasmine invest for each son on June 1 to provide them the desired allowance?
(ii) Create a timeline of events for each of the sons.
(iii) What is the total amount invested on June 1?

Answer 1

a. Allowance each of the boys will receive per month based on their parents’ assumptions of price increases:
Stepehen	1000
Jack(1000*1.08)	1080
Danny(1080*1.1)	1188

b. i..Investment for each son:

Stephen

Sum at the start mth.(ie.Sep.1) After he turned 18 at 4% p.a. ie. 4%/12=0.0033 per mth.for 4yrs.*12=48 mths.-- for equal monthly amt. of $ 1000

PV of the beginning of the mth. Annuity as above=(1000*(1-1.0033^-48)/0.0033)*(1.0033)=

44470.23

PV of the investment on June 1 (Yr.0) will be

no.of mths.=(12mths.*6 yrs.)+ 3mths until Sep.1

72+3=75 mths.

PV at Yr. 0 of the investment on June 1 will be

44470.23/1.0033^75=

34734.29

34734

Jack

Sum at the start mth.(ie.Sep.1) After he turned 18 at 4% p.a. ie. 4%/12=0.0033 per mth.for 4yrs.*12=48 mths.-- for equal monthly amt. of $ 1000

PV of the above beg.of the mth annuity =(1080*(1-1.0033^-48)/0.0033)*(1.0033)=

48027.85

PV of the investment on June 1 (Yr.0) will be

no.of mths. From Jun 1 of Yr.0 =(12mths.*9 yrs.)+ 3mths until Sep.1

108+3=111 mths.

PV at Yr. 0 of the investment on June 1 will be

48027.85/1.0033^111=

33317.54

33318

Danny

Sum at the start mth.(ie.Sep.1) After he turned 18 at 4% p.a. ie. 4%/12=0.0033 per mth.for 4yrs.*12=48 mths.-- for equal monthly amt. of $ 1000

PV of the above beg.of the mth.annuity=(1188*(1-1.0033^-48)/0.0033)*(1.0033)=

52830.64

PV of the investment on June 1 (Yr.0) will be

no.of mths. From Jun 1 of Yr.0 =(12mths.*11 yrs.)+ 3mths until Sep.1

132+3=135 mths.

PV at Yr. 0 of the investment on June 1 will be

52830.64/1.0033^135=

33863.06

33863

(ii)Timeline of events for each of the sons
Stephen
Year	Age
Apr. Yr.0	12
Jun Yr.6	18
From Sep.1 Yr.6	for 48 mths.
Jack
Apr. Yr.0	9
Jun Yr.9	18
From Sep.1 Yr.9	for 48 mths.
Danny
Apr. Yr.0	7
Jun Yr.11	18
From Sep.1 Yr.11	for 48 mths.

(iii) Total amount invested on June 1
Stephen	34734
Jack	33318
Danny	33863
Total	101915