Chapter 6, Problem 62RE

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

10th Edition
Ron Larson
ISBN: 9781305860919

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 = $15 , 000 , r = 5 % To determine To calculate: The charitable endowment amount that is set up to pay amount P=$15,000 at the rate of annual interest r=5%.

Explanation

Given Information:

Provided information is:

Payment is P=$15,000 and rate of annual interest is r=5%. 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, Payment, P=$15,000

Rate of annual interest, r=5%

Interest in decimal form is,

r=5%=5100=0.05

Now, use the formula,

Present value=P0ertdt

Substitute \$15,000 for P and 0

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