David and Briana have three children: Micah $($age $12),$ Lilly $($age $8)$ and Moe $($age $6).$

The children attend public school. The Fosters would like to plan for paying tuition for a College Education for each child for $5$ years, each beginning at Age $18,$ at Maryland State University.

They do not want to count on qualifying for financial aid to send their children to college but would like to know about financial aid. Assumptions In your research you have discovered that: $-$ Current Tuition is $ $20,000$ per year at MD State. $-$ While you believe they can earn $8\mathrm{.}5\%$ on their education savings for college, you also know college inflation costs are expected to be $6\%$ annually. $-$

Briana$$s Dad set up $529$ accounts for Micah and Lilly when they were born. Micah$$s has $$7,500$ in it and Lilly$$s has $$5,500.$ He has committed to opening a $529$ for Moe this week and investing $$3,000.$ He has indicated he would not be contributing any other money for their education. The $529$ accounts are expected to earn $8\mathrm{.}5\%.-$ You should be able to perform all calculations using either the Uneven Cash Flow Method or the Traditional Method, found in Chapter $8$ of your Fundamentals textbook.

$1)$ Calculate the cost of a $5-$year education for each child. Show the steps performed to get your answer.

$2)$ Calculate the amount they would have to invest today in a lump sum to fully fund college for each in the future. Show the steps performed to get your answer.

$3)$ Calculate the annual savings amount required for each if the Fosters chose not to fund education today with a lump sum and were willing to pay through the end of college for each. Show the steps performed to get your answer.