Question: A perpetuity is a periodic sequence of payments that continues forever. The capital value of the perpetuity is the sum of the present values of

A perpetuity is a periodic sequence of payments that continues forever. The capital value of the perpetuity is the sum of the present values of all future payments.

Consider a perpetuity that promises to pay P dollars at the end of each month. (The first payment will be received in 1 month.) If the interest rate per month is r, the present value of P dollars in k months is P(1 + r)^-k. Find a simple formula for the capital value of the perpetuity.

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