UMS, an elite private school in Texas, currently has an endowment of 1.6 billion dollars. The university has agreed to fund new academic initiatives over the next 10 years by taking a draw from the endowment at the end of each year, beginning one year from now (at the end of year 1). The university will calculate the amount of draw using a formula based on the year-end value of the endowment. The table below summarizes how large a draw the university will take based on the endowment's year-end value.

Amount of Endowment (year-end)	Draw (%) of Endowment
0 -- $1,500,000,000	0%
$1,500,000,000 -- $2,000,000,000	1%
$2,000,000,000 -- $2,500,000,000	2%
$2,500,000,000 --	3%

Assume the university has conservative investments with a mean annual (or one-year) return of 6% and a standard deviation of 5%, and assume future returns are normally distributed. Based on a simulation model with N = 10,000 trials, answer the following questions:

a. What is the average endowment balance at the end of year 10, immediately after taking any final year- ending draw?

b. How many total dollars, on average, are drawn from the endowment over the ten-year period (include the final draw at the end of year 10)? Do not discount!

c. What is the probability that the final year's draw is at the maximum 3% level?