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Alice and Luka spend X dollars each to purchase annuities. Alice buys a perpetuity-immediate, which makes annual payments of 20. Luka buys a 15-year annuity-immediate,

Alice and Luka spend X dollars each to purchase annuities. Alice buys a perpetuity-immediate, which makes annual payments of 20. Luka buys a 15-year annuity-immediate, also with annual payments. The first payment is 53, with each subsequent payment k% larger than the previous years payment. Both annuities use an annual effective interest rate of k%. Calculate k.

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