Find a formula for the capital value of a perpetuity involving payments of P dollars paid at the end of each investment period into a fund that earns interest at the annual rate of k% compounded continuously.
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Hint: If we are given a perpetuity involving payments of P dollars each, paid at the end of each of m periods per year into a fund that earns interest at the nominal rate of k% per year compounded m times a year, the following holds:
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The present value of the nth payment is
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The capital value is
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Using the fact that the above series is a geometric series, its sum is
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What will be an ideal response?
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