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.

Find the capital value of an asset that generates income at the rate of $5000 per year, assuming an interest rate of 10%.

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