$2$a$.(10$ points$)$ As a limited partner, you committed $$1,000$ to a $10-$year private equity fund. The first capital call for $$750$ came one year after the creation of the fund and it was completely invested in a portfolio company. The second capital call for $$250$ came two years after the creation of the fund and it was completely invested in a portfolio company. Since there were no management fees, you were promised a compound $8\%$ return on your entire investment for as long as it was invested. The portfolio companies you were invested in were at time $10,$ the end of the fund$$s life. The first purchased was sold for $6$X the purchase price and the second purchased was sold for $4$X the purchase price. The agreed split of the carried interest was $25\%$ to the GP and $75\%$ to the LP$.$ How much cash will you receive at time $10?$ What is your IRR?

b$.(10$ points$)$ After the LP has signed the LP agreement with all its details, what are the biggest uncertainties that will affect the cash the LP will receive at time $10?$ Answer this for each of the three phases in the timeline we drew for the life of the fun