# Answer on Integral Calculus Question for nicholas

Question #7317

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, 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

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, 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

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