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John will make five deposits, of X each, at the beginning of each of the next five years, into a fund that earns a nominal

John will make five deposits, of X each, at the beginning of each of the next five years, into a fund that earns a nominal rate of discount of 8% convertible semiannually. The fund must provide for a perpetuity of annual payments of $100 beginning at the end of the 6th year and increasing by $50 each year. Determine the smallest amount X can be.

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