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I do not need excel solution. Please give me the theoretical solution. Payments of 1000 are invested at the end of each year for 5

I do not need excel solution. Please give me the theoretical solution.

Payments of 1000 are invested at the end of each year for 5 years. The payments earn interest at an annual effective rate of 10%. The interest can be reinvested at an annual effective rate of 6% in the first 4 years and at an annual rate of k thereafter. The amount in the fund at the end of 5 years is 6090. Calculate k.

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