The capital value of an asset such as a machine is sometimes defined as the present value of all future net earnings of the asset.The actual lifetime of the asset may not be known, and since some assets last indefinitely, the capital value of the asset may be written in the form $\int_{0}^{\infty} K(t) e^{-r t} d t$ ,
where K(t)is the annual rate of earnings produced by the asset at time t, and r is the annual interest rate, compounded continuously.Find the capital value of an asset that generates income at a rate of $1000 per year, with an interest rate of 9%.Round to the nearest dollar.

Question

Quizplus · Accepted Answer

The Answer of The capital value of an asset such as a machine is sometimes defined as the present value of all future net earnings of the asset.The actual lifetime of the asset may not be known, and since some assets last indefinitely, the capital value of the asset may be written in the form $\int_{0}^{\infty} K(t) e^{-r t} d t$ ,
where K(t)is the annual rate of earnings produced by the asset at time t, and r is the annual interest rate, compounded continuously.Find the capital value of an asset that generates income at a rate of $1000 per year, with an interest rate of 9%.Round to the nearest dollar.

The Capital Value of an Asset Such as a Machine ∫0∞K(t)e−rtdt\int_{0}^{\infty} K(t) e^{-r t} d t∫0∞​K(t)e−rtdt

The Capital Value of an Asset Such as a Machine $\int_{0}^{\infty} K(t) e^{-r t} d t$