The capital value of an asset such as a machine is sometimes defined as the present value of all future net earnings. The actual lifetime of the asset may not be known, and since some assets may last indefinitely, the capital value of the asset may be written in the form

where r is the annual rate of interest compounded continuously.

Construct a formula for the capital value of a rental property that will generate a fixed income at the rate of K dollars per year indefinitely, assuming an annual interest rate of r.

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[capital value] = 0 K(t)et dt,