$6.$ Meredith Shomers manages scholarship endowments for a major public university.

Presently, she is trying to determine how much scholarship money may be awarded from

an endowment with a current balance of $$538,000.$ The endowment$$s funds are invested in

a portfolio whose annual return varies and may be represented as a normally distributed

random variable with a mean of $6\%$ and standard deviation of $2\%.$ The legal terms of the

endowment require Meredith to determine a constant scholarship payment amount from the

endowment that, if made in each of the next $10$ years, would result in only $5\%$ chance of the

endowment$$s ending value dropping below its current value. Assume scholarship payments

are withdrawn from the fund at the end of each year.

a$.$ Create a spreadsheet model for this problem.

b$.$ What is the maximum scholarship payment that should be made in the current year?

explain with clear spreadsheet along with formulas and steps from start till end in detail. Thank You