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Question: You borrow 1,000 at an annual effective interest rate of 4%, and agree to repay it with 3 annual installments. The amount of each payment in the last 2 years is set at twice that in the first year. At the end of 1 year, you have the option to repay the entire loan with a final payment of X, in addition to the regular payment. This will yield the lender an annual effective rate of 4.5% over the 1-year period. Calculate X.

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