Chapter 6.1, Problem 7CP

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10th Edition

Ron Larson

ISBN: 9781305860919

Textbook Problem

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Checkpoint 7

A company expects its income during the next 10 years to be given by *c*(*t*) = 20,000*t*, for 0 ≤ *t* ≤ 10. Assuming an annual inflation rate of 5%, what is the present value of this income?

To determine

**To calculate:** The present value of the income if the expected income of company during next 10 years is given by

Explanation

**Given Information:**

The expected income of company during next 10 years is given by

**Formula used:**

1. If *r* (in decimal form), then the present income over

2. The integration by parts

Where,

**Calculation:**

Consider the provided information that the expected income of company during next 10 years is given by

Now calculate the present value by using formula,

Consider the indefinite integral

Here,

First find

On further solving,

Find

Differentiate both side with respect *t*;

And,

Apply integration by parts formula and substitute equation (1) and (2) in

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