   Chapter 6, Problem 64RE ### Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919

#### Solutions

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

10th Edition
Ron Larson
ISBN: 9781305860919
Textbook Problem
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# Present Value You are considering buying a franchise that yields a continuous flow of profit at the rate of $100,000 per year. Assuming an annual interest rate of 6% compounded continuously, what is the present value of the franchise (a) for 15 years and (b) forever? (a) To determine To calculate: The present value of the franchise if the continuous flow of profit is at the rate of$100,000 per year and the interest rate is 6% compounded continuously for 15 years.

Explanation

Given Information:

Provided information is:

Profit, P=$100,000 per year Interest rate is, r=6% And time span is 15 years. 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 data, Profit, P=$100,000 per year

Interest rate is, r=6%

Interest in decimal form is:

r=6%=6100=0.06

And time span is 15 years.

Use the formula for the present value,

Present value=P0tertdt

Substitute $100,000 for P and 0 (b) To determine To calculate: The present value of the franchise if the continuous flow of profit is at the rate of$100,000 per year and the interest rate is 6% compounded continuously forever.

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