   Chapter 6.1, Problem 77E ### 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 A professional athlete signs a four-year contract in which the earnings c can be modeled by c   = 3 , 000 , 000   +   750 , 000 t , where t represents the year.(a) Find the actual value of the athlete’s contract.(b) Assuming an annual inflation rate of 5 % , what is the present value of the contract?

(a)

To determine

To calculate: The actual value of the contract if a professional athlete signs a contract for the 4 years where the earnings is model by c=3000000+750000t.

Explanation

Given information:

A professional athlete signs a contract for the 4 years where the earnings is model by

c=3000000+750000t.

Formula used:

Actual income over the t1 years can be calculated as:

Actual income over t1 years=0t1c(t)dt

Calculation:

Consider the provided statement:

Expected income model is c=3000000+750000t

It is provided that t1=4 years.

Now find Actual income with the help of the formula: Actual income over t1 years=0t1c(t)dt

Substitute the value of t1=4, and c=3000000+750000t in the above function

(b)

To determine

To calculate: The present value if a professional athlete signs a contract for the 4 years where the earnings is model by c=3000000+750000t and inflation rate is 5%.

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