   Chapter 6, Problem 61RE ### 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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# Endowment In Exercises 61 and 62, determine the amount of money required to set up a charitable endowment that pays the amount P each year indefinitely for the annual interest rate r compounded continuously. P = $8000 , r = 3 % To determine To calculate: The charitable endowment amount that is set up to pay amount P=$8,000 at the rate of annual interest, r=3%.

Explanation

Given Information:

Provided information is,

Amount is P=$8,000 and interest rate is r=3%. Formula used: Present value of Perpetuity: Present value=P0ertdt Here, P is the size of each annual payment and r is the annual interest rate in decimal form. If on the interval [a,), the function is continuous, then af(x)dx=limbabf(x)dx Calculation: Consider the provided data, Amount P=$8,000

The rate of annual interest, r=3%.

Interest in decimal form will be,

r=3%=3100=0.03

Now, use the formula,

Present value=P0ertdt

So, the amount needed to set up the charitable endowment will be,

08000e0

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