Before starting the new job, Hassan Mustafa and his wife, Dana, 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. Hassan and Dana wanted to ensure enough funds were available for their studies.Hassan and Dana 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, Hassan and Dana 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 $18.$Hassan and Dana 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 $4\mathrm{.}0\%$ compounded monthly, from the day of the investment until the three boys had each completed their four years of education. Hassan and Dana thought this sounded reasonable.So$,$ on June $1,$ they deposited the sum of money necessary to finance their sons' post$-$secondary educations$\mathrm{.}4.$ How much allowance will each of the boys receive per month based on their parents' assumptions of price increases?$5.$ a$.$ How much money must Hassan and Dana invest for each son on June $1$ to providethem the desired allowance?b$.$ Create a timeline of events for each of the sons..What is the total amount invested on June $1?$