a. Derek invested $12,000 in a mutual fund five years ago. He received a dividend check for $1,000 after the first year. He received $750 after the second year. At the end of the third year, he received a check for $1,500. After the fourth year, he collected $750. His final dividend check of $1,000 was received at the end of the fifth year. Assume that Derek sold the mutual fund at the end of the fifth year for $18,000. What was Derek's internal rate of return?

b. Kristy purchased shares of a mutual fund five years ago. She has since made the following additional transactions:

End of year 2, invested additional $2,500 in the fund

End of year 3, invested additional $9,000 in the fund

End of year 5, redeemed all of he shares in the fund, receiving $16,000

Kristy just told you she achieved an annual return of 9 percent in this investment. If Kristy is correct, what was her initial investment in the fund?