Answer Happy

Capital Value The capital value of an asset is often defined as the present value of all future net earnings of the asset. In other words, suppose an asset provides a continuous money flow that is invested in an account earning a certain rate of interest. A lump sum is invested in a second account earning the same rate of interest, but with no money flow, so that as t→∞, the amounts in the two accounts approach each other. The lump sum necessary to make this happen is the capital value of the asset. If R(t) gives the annual rate at which earnings are produced by an asset at time t, then the present value formula from Section 3 gives the capital value as ∫0∞​R(t)e−rtdt where r is the annual rate of interest, compounded continuously. 1. Suppose income from a rental property is generated at the annual rate of $20,000 per year. Find the capital value of this property at an interest rate of 4% compound continuously.