   Chapter 6.1, Problem 73E ### 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 have just won $2,000,000 in a state lottery. You will be paid an annuity of$80,000 a year for 25 years. When the annual rate of inflation is 5%, what is the present value of this income?

To determine

To calculate: The present value if someone just won $2000000 and it will be paid an annuity of$80000 over the time interval of 25 years and the inflation rate is r=5%.

Explanation

Given information:

Someone just won $2000000 in a state lottery. They paid an annuity of$80000 a year for 25 years. The annual rate of inflation is r=5%.

Formula used:

Present value can be calculated as:

Present value=0t1c(t)ertdt

Integration by parts:

udv=uvvdu

Common integration using integration by parts

xneaxdx

Where u=xn and dv=eaxdx

Calculation:

Consider the provided statement:

The annuity paid is \$80000

It is provided that t1=25 years and the inflation rate is r=5%.

Now find Present value with the help of the formula: Present value=0t1c(t)ertdt

Substitute the value of t1=5, r=0

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