Explanation Given information: A large farm with a known reservoir of gas beneath the ground sells the gas rights to a company for a guaranteed payment at the rate of 10 , 000 e 0.04 t dollars per year and the interest rate is 12 % . Explanation: By using the formula for present value of the stream of income, Present Value of a Continuous Stream of Income: [ present value ] = ∫ T 1 T 2 K ( t ) e − r t d t , where K ( t ) is the annual rate of income at time t , r is the annual interest rate and T 1 to T 2 (years) is the time period of the income stream. Here K ( t ) = 10 , 000 e 0.04 t and r = 12 % = 0.12 Substitute the values in the above formula. Present value = ∫ 0 ∞ ( 10 , 000 e 0.04 t ) e − 0.12 t d t ∫ 0 ∞ 10 , 000 e − 0.08 t d t = lim b → ∞ [ ∫ 0 b 10 , 000 e − 0

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Chapter 9.6, Problem 50E

To determine

The present value of the perpetual stream of income when a large farm with a

known reservoir of gas beneath the ground sells the gas rights to a company for a guaranteed

payment at the rate of 10,000e0.04t dollars per year and assuming the interest rate is 12%

compounded continuously.

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Chapter 9.6, Problem 49E

Chapter 9, Problem 1FCCE

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Chapter 9 Solutions

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The present value of the perpetual stream of income when a large farm with a known reservoir of gas beneath the ground sells the gas rights to a company for a guaranteed payment at the rate of 10 , 000 e 0.04 t dollars per year and assuming the interest rate is 12 % compounded continuously.

Solution Summary: The author explains the formula for present value of a perpetual stream of income: 125,000.

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The present value of the perpetual stream of income when a large farm with a

known reservoir of gas beneath the ground sells the gas rights to a company for a guaranteed

payment at the rate of 10,000e0.04t dollars per year and assuming the interest rate is 12%

compounded continuously.

Want to see the full answer?

Chapter 9 Solutions

The present value of the perpetual stream of income when a large farm with a known reservoir of gas beneath the ground sells the gas rights to a company for a guaranteed payment at the rate of 10 , 000 e 0.04 t dollars per year and assuming the interest rate is 12 % compounded continuously.

Solution Summary: The author explains the formula for present value of a perpetual stream of income: 125,000.

Concept explainers

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The present value of the perpetual stream of income when a large farm with a known reservoir of gas beneath the ground sells the gas rights to a company for a guaranteed payment at the rate of 10,000e0.04t dollars per year and assuming the interest rate is 12% compounded continuously.

Want to see the full answer?

Chapter 9 Solutions

The present value of the perpetual stream of income when a large farm with a

known reservoir of gas beneath the ground sells the gas rights to a company for a guaranteed

payment at the rate of 10,000e0.04t dollars per year and assuming the interest rate is 12%

compounded continuously.