Your aunt consults with you about her retirement 12 years from now. She currently has $800,000 to invest. Over the next 12 years she will withdraw $25,000 from her investments every year (withdrawals done at the end of the year). She will also gift $30,000 to her nephews and nieces at the end of the 7th and 14th years (lucky you!). After retiring 12 years from now, she will withdraw a constant amount every year for the next 18 years so that she has zero savings at the end of 18 more years (that is 30 years from today. She expects that Social Security will pay for her expenses if she lives beyond that point).

Withdrawals for each year are made at the end of each year. Investments earn a 6% return per year, and there are no taxes.

What will be the value of your aunt's investments at the end of the 12th year (after the end of the year withdrawal for the 12th year has been made)?

Explanation: Just think of your aunt's investments as composed of 4 parts: (1) first part which pays the annuity till the 12th year (2) second part that pays for the gift at the 7th year (3) third part that pays the gift at the 14th year (4) that which is left over from initial total investment after the first three part has been deducted. Now grow the third and fourth parts at the rate (1+r) per year till the end of the 12th year.