Williams Family Case Study $($Time Value of Money Case Study$)$ Williams Family is composed of John $($father$),$ Anna $($mother$),$ and $5-$year$-$old son Vivan. John is a partner in the family owned commercial painting business and Anna is a housewife. John and Anna became concerned of their spending, that they are not putting enough money for their son's future education needs as well as their own retirement purpose. Therefore, they planned to visit to the financial planner named Koegh plan $($retirement plan for self$-$employed individuals and small businesses in the US$),$ but they did not account for Vivan's education. John's cash inflows are $$85,000$ a year. John is an alumnus of Darden University $($Tuition $=$ $$20,000$ per year$).$ Anna graduated from University of South Carolina $($Tuition $=$ $$2,500$ per year$)$ The couple wants to send Vivan to either school when he turns $18,$ with a slight preference towards Darden. Vivan's Tuition fee is expected to increase at an annual rate of $5\%.$ Living expenses are estimated to be $$6000$ per year for both schools $($expecting to grow $3\%$ per year$)$ The couple can deposit their money into a growth oriented mutual fund at Neuberger and Berman Management, Inc. $($historically earning $12\%$ per annum$).$ Assume you as Koegh the financial planner, answer the below queries mentioned by Williams family. $1.$ How much will the tuition and living expenses be per year when Vivan is ready to attend? Give an answer for each university. $2.$ Once Vivan starts college what will his total expenses be in each of his four years? Again, give an answer for each university. $3.$ How much money will John and Anna have to deposit per month to allow Vivan to attend Darden University? How much money will have to be deposited per month to allow Vivan to attend the University of South Carolina? $($Consider the cost of all four years.$)4.$ What if the Williams feel the Neuberger & Berman mutual fund will only yield $10$ per cent? How much will have to be deposited per month in order for Vivan to attend each college? What is the relationship between the amount that must be deposited monthly by the parents and the future increases in both tuition and living expenses?