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

Answer to the part a

Stephen would receive $ 1,000 p.m. (given)

Jack would get 8% more than Stephen. Hence he would get $ 1,000 x (1 + 8%) = $ 1,080 p.m.

Danny would get 10% more than Jack. Hence he would get $ 1,080 x (1 + 10%) = $ 1,188 p.m.

Answer to the part b (i)

Stephen's age now = 12 years. Therefore time to reach 18 years = 6 years from now.

Jack's age now = 9 years. Therefore time to reach 18 years = 9 years from now.

Danny's age now = 7 years. Therefore time to reach 18 years = 11 years from now.

Time period for Equal Monthy Installments (beginning) = 4 years

PV of Investment required to pay Stephen $ 1,000 p.m. beginning allowance, at the year he turns 18

= PV6 = $ 44,436

Therefore present value of the investment required now = PV0  = $ 34,622

PV of Investment required to pay Jack $ 1,080 p.m. beginning allowance, at the year he turns 18

= PV9 = $ 47,991

Therefore present value of the investment required now = PV0  = $ 33,170

PV of Investment required to pay Stephen $ 1,188 p.m. beginning allowance, at the year he turns 18

= PV11 = $ 52,791

Therefore present value of the investment required now = PV0  = $ 33,686

Note : Present Value Calculations are based on :

1. Timelines in months as mentioned in part b (ii).

2. Interest Rate of 4% p.m. compounded monthly. (0.333% p.m.)

3. Equal Monthly allowance as mentioned in part a for each son.

4. Present Value Calculations are end-of-the-period-type for dormant period (no allowance is received) and beginning of the period type for period during college starts.

5. Sample PV formulae used in excel =PV(4%/12,48,1000,0,1) for calculation of Investment required for paying Stephen's monthly allowance at PV6. Similarly calculated for each son.

6. Sample PV formulae used in excel =PV(4%/12,75,0,44436,0) for calculation of PV0 of Investment required for paying Stephen's monthly allowance beginning PV6. Similarly calculated for each son

Answer to the part b (ii)

Timelines
Stephen	|--------------75 months -------------|--------------------------48 months---------------------------|
April - Year 0	June, 1 - Year 0	September, 1 - Year 6	August, 1 - Year 10
Stephen turns 12	Stephen's Corpus Invested	Stephen starts college. Receives 1st installment of $ 1,000	Last installment Stephen receives
Jack	|--------------111 months ------------|--------------------------48 months---------------------------|
January - Year 0	June, 1 - Year 0	September, 1 - Year 9	August, 1 - Year 13
Jack turns 9	Jack's Corpus Invested	Jack starts college. Receives 1st installment of $ 1,080	Last installment Jack receives
Danny	|--------------135 months -----------|---------------------------48 months---------------------------|
March - Year 0	June, 1 - Year 0	September, 1 - Year 11	August, 1 - Year 15
Danny turns 7	Danny's Corpus Invested	Danny starts college. Receives 1st installment of $ 1,188	Last installment Danny receives

Answer to the part b (iii)

PV of all the above investments on June 1, in current year = PV0 = $ 34,622 + $ 33,170 + $ 33,686

= $ 101,477

Hence Total Investment required on June 1 = $ 101,477