If an investment promises to provide A dollars at time t in the future, we can define the present value P as the amount that would have to be invested to generate A dollars after time t, assuming an interest rate r. This can be expressed as Pe^(rt) = A, or P = Ae^(-rt). The capital value of an asset can be defined as the present value of all future income from that asset. If the asset lasts indefinitely, the capital value can be written as CV=∫(lower limit:0,upper limit:infinity) K(t)e^(-rt)dt, where K(t) is the annual rate of income from the asset, r is the annual rate of interest,

Question

If an investment promises to provide A dollars at time t in the future, we can define the present value P as the amount that would have to be invested to generate A dollars after time t, assuming an interest rate r. This can be expressed as Pe^(rt) = A, or P = Ae^(-rt). The capital value of an asset can be defined as the present value of all future income from that asset. If the asset lasts indefinitely, the capital value can be written as CV=∫(lower limit:0,upper limit:infinity) K(t)e^(-rt)dt, where K(t) is the annual rate of income from the asset, r is the annual rate of interest,

anonymous · Answer

and t is the time in years. Suppose I sell the mining rights to a piece of land to a company for a payment of 10000e^(0.04t) dollars per year. Find the present value of this income, assuming interest of 12% annually.

anonymous · Answer

p=10000e^(.04t) r=.12 t=1