Question

Victor And Jasmine were Discussing How to plan for their three young sons' university education

SE STUDY Planning for University 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 oft 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 1. How much allowance will each of the boys receive per month based on their par- ents' assumptions of price increases? 2. (a) How much money must Victor and Jasmine invest for each son on June 1 to provide them the desired allowance? (b) Create a timeline of events for each of the sons (c) What is the total amount invested on June 1?

If so how can this be done on a BA II Plus Financial Calculator?

Answer 1

Given ROI is 4% p.a. compounded monthly and investment commences by 1st June 2019 (Assumed).

The timeline of events is as under.

Name	Birthday	Age on Birthday	Allowance / Month	Total Allowance	Turns 18 on	Funds Required by	Investment Commences By
Stephen	Apr-19	12	1000	48,000	Apr-25	Sep-25	Jun-19
Jack	Jan-19	9	1080	51,840	Jan-28	Sep-28	Jun-19
Dany	Mar-19	7	1188	57,024	Mar-30	Sep-30	Jun-19

As per Bank Manager's statement, investment will be from now till the boys have completed their 4 years of education. Based on this, we are calculating the future values of cash flows required and discounting to time 0 as shown below.

Year	Stephen	Jack	Dany	Total	PV
2025	4000	0	0	4000	3091
2026	12000	0	0	12000	9029
2027	12000	0	0	12000	8676
2028	12000	4320	0	16320	11297
2029	8000	12960	0	20960	14026
2030	0	12960	4752	17712	11319
2031	0	12960	14256	27216	16771
2032	0	8640	14256	22896	13591
2033	0	0	14256	14256	8111
2034	0	0	9504	9504	5230
Total	48000	51840	57024	156864	101140

The sum of present value of future cash flows gives the total investment required on 1st June 2019 i.e.) 101,140.

For monthly compounding, present value is calculated using formula PV = CF / (1+ intrate / 12)^MonthNo.

MonthNo starts from 76 and ends with 183, i.e) Sep 2025 and Aug 2034

Please note the discounting was done on monthly basis on cash flows. Due to space constraint, annual cash flows is shown.