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Youve just turned 40 years old, and youve worked very hard. Its paid off. Youre both professionally and financially successful, and youd like to leave a long lasting legacy after you retire. Youve decided to fund an infinite stream of college scholarships for under privileged students. More specifically, in order to fund the scholarships, youve decided to make equally sized annual deposits into an investment account that is expected to earn 7% per year, forever. Youll make the first deposit of $50,000 into the account on your 45th birthday. Thereafter youll make nine additional deposits of the same size on your 46th, 47th, and 54th birthdays. After your 10th deposit, youll let the money remain in the account, where it will continue to earn 7% per year. Youve decided to have the scholarships begin on your 60th birthday, and they will continue every year thereafter - forever. More specifically, on your 60th birthday, youll withdraw a total of $100,000 which will be immediately distributed to students in need. Withdraws from the account will continue every year thereafter (forever) and youd like to have them grow (or shrink) at a constant rate each year. Throughout the course of the investment (from age 40 to the end of time) all money in the account will earn 7% per year. Part (A) Immediately before the first withdraw, how much money is there in the account? Part (B) Determine the growth rate, g, associated with the size of the never ending scholarship withdraws. For example, is there enough money saved to have the size of the scholarships grow at 4.354% per year? 9.205% per year? -4.275% per year? Determine the growth rate to at least 4 significant digits. Enter your answer as a decimal, not as a percent.

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