Chapter 6.4, Problem 37E

### Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919

Chapter
Section

### Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919
Textbook Problem
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# Present Value A business is expected to yield a continuous flow of profit at the rate of $500,000 per year. Assuming an annual interest rate of 9% compounded continuously, what is the present value of the business(a) for 20 years?(b) forever? (a) To determine To calculate: The present value of the business if the continuous flow of profit at rate of$500,000 per year and interest rate is 9% compounded continuously for 20 years.

Explanation

Given Information:

Provided information is:

Profit is P=$500,000 and annually interest rate is r=9%. Formula used: Present value of Perpetuity: Present value=P0tertdt Here, P is the size of each annual payment, t is the time and r is the annual interest rate in decimal form. Calculation: Consider the provided information and recall the formula for present value. Present value=P0tertdt Interest in fraction form is: r=9%=9100=0.09 Substitute$500,000 for P and 0

(b)

To determine

To calculate: The present value of the business if the continuous flow of profit at rate of \$500,000 per year and interest rate is 9% compounded continuously for forever.

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