Chapter 8, Problem 87RE

### Calculus (MindTap Course List)

11th Edition
Ron Larson + 1 other
ISBN: 9781337275347

Chapter
Section

### Calculus (MindTap Course List)

11th Edition
Ron Larson + 1 other
ISBN: 9781337275347
Textbook Problem

# Present Value The board of directors of a corporation is calculating the price to pay for a business that is forecast to yield a continuous flow of profit of $500,000 per year. The money will earn a nominal rate of 5% per year compounded continuously. The present value of the business for t 0 years isPresent value = ∫ 0 t 0 500 , 000 e − 0.05 t d t . (a) Find the present value of the business for 20 years.(b) Find the present value of the business in perpetuity (forever). (a) To determine To calculate: For the function P=0to500000e0.05tdt; the present value of the business for 20 years Explanation Given: Profit per year is$500,000.

Rate is 5% per year compounded continuously.

The present value function is:

P=âˆ«0to500000eâˆ’0.05tdt

Formula used:

The integration formula:

âˆ«ef(x)dx=ef(x)(1fâ€²(x))

Calculation:

Solve the integral

P=âˆ«0to500000eâˆ’0.05tdt as below:

P=âˆ«0to500000eâˆ’0.05tdt=500000âˆ«0toeâˆ’0

(b)

To determine

To calculate: The present value of the business in perpetuity for the function P=0to500000e0.05tdt.

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