Problem:
Today is Sarah's 30th birthday. Five years ago, Sarah opened a brokerage account when her grandmother gave her $25,000 for her 25th birthday. Sarah added $2,000 to this account on her 26th birthday, $3,000 on her 27th birthday, $4,000 on her 28th birthday, and $5,000 on her 29th birthday.
Sarah's goal is to have $400,000 in the account by her 40th birthday. Starting today, she plans to contribute a fixed amount to the account each year on her birthday. She will make 11 contributions, the first one will occur today, and the final contribution will occur on her 40th birthday. Complicating things somewhat is the fact that Sarah plans to withdraw $20,000 from the account on her 35th birthday to finance the down payment on a home. How large does each of these 11 contributions have to be for Rachel to reach her goal? Assume that the account has earned (and will continue to earn) an effective return of 12 percent a year.