## Annuity Due Problem

Joseph and Mireille Lacarte were discussing how to plan for their three young sons’ university education. Steve turned twelve years old in April, Joe turned nine in January, and Drew turned seven in March. Although university was still a long way off for the boys, Joseph and Mireille wanted to ensure enough funds were available for their studies.

Joseph and Mireille 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, Joseph and Mireille 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.

Steve would receive an allowance of $1000 per month starting September 1 of the year he turns eighteen. Joe would receive an allowance that is 8% more than Steve’s allowance. He would also receive it at the beginning of September 1 of the year he turns eighteen. Drew would receive an allowance that is 10% more that Joe’s at the beginning of September of the year he turns eighteen. Joseph and Mireille visited their local bank manager to fund the investment that would compensate the boys’ allowances for university. The bank manager suggested an investment paying interest of 5.5% compounded monthly from now until the three boys had each completed their four years of education. Joseph and Mireille 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’ postsecondary educations. Questions 1. How much allowance will each of the boys receive per month based on their parents’ assumptions of price increases? 2. a. How much money must Joseph and Mireille invest for each son on June 1 in order to provide them the desired allowance? b. What is the total amount invested on June 1? ----- Alright, so I think I've got #1 finished. Steve would recieve$1000, Joe would receive $1080 and Drew would be getting$1188. Hopefully this is right or it could have been what was messing me up this whole time.

I'm now stuck at what to do in order to calculate 2-a. I know I've got to use either the future value or present value annuities due formula, which I have access to, but I keep getting numbers that are way out of sync with what I think they should be. I must be doing something really wrong.

Can anyone show me an example of how to use the formulas with one of the sons so I can work on the last two myself? I'd really appreciate any help!