Present Value for Perpetuities

We present the first way of calculating present value by examining the case of a perpetuity, which is an asset like land that lasts forever and pays $N each year from now to eternity. We are seeking the present value (V) if·the interest rate is i percent per year.

where the present value is the amount of money invested today that would yield exactly $N each year. This is simply

This says’that if the interest rate is always 5 percent per year. an asset yielding a constant stream of income will sell for exactly 20 (= 1 + 5/100) times its annual income. In this case, what would be the present value of a perpetuity yielding $100 every year? At a 5 percent interest rate its present value would be $2000 (= $100 + 0.05)

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