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Dr. Jones is a billionaire and an amateur mathematician. Today, she wants to invest 80 million dollars at a fixed annual interest rate of 10%

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Dr. Jones is a billionaire and an amateur mathematician. Today, she wants to invest 80 million dollars at a fixed annual interest rate of 10% and use this fund to set up a "Nobel prize" for mathematicians: in each year, she awards a sum of money to the most outstanding mathematician. To combat inflation, the size of the prize is x for the first year, 1.045x in the second year, and $1.045-x in year t. Suppose that the first prize is scheduled to be given out immediately and Dr. Jones wants this to become a legacy that lasts forever, what is the highest possible value of x in millions of dollars? (For example, if your answer is 5 million, please enter 5 without adding "million".)

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