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On January 1, 1998, John deposited $ 1000 into Bank X to earn interest at rate i per annum compounded quarterly. On January 1, 2003, he transferred his account to Bank Y to earn interest at rate j per annum compounded semiannually. On January 1, 2006, the balance at Bank Y is $ 2074.81. If John could have earned interest at rate j per annum compounded semiannually for the entire eight years, his balance would have been $ 2318.5. Calculate the ratio of j to i.

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