Problem: Mary deposits 1000 into a fund at the beginning of each year for 10 years. At the end of 15 years, she makes an additional deposit of X. At the end of 20 years, Mary uses the accumulated...

Problem:

Mary deposits 1000 into a fund at the beginning of each year for 10 years. At the
end of 15 years, she makes an additional deposit of X. At the end of 20 years, Mary
uses the accumulated balance in the fund to buy a perpetuity-immediate with annual
payments of 2000 for 10 years, and 1000 per year thereafter. The annual effective
interest rate is 7%.
(i) Calculate the time value of the perpetuity at the end of 20 years.
(ii) Determine X.