Chapter 6.4, Problem 35E

### 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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# Scholarship Fund You want to start a scholarship fund at your alma mater. You plan to give one $18,000 scholarship annually beginning one year from now, and you have at most$400,000 to start the fund. You also want the scholarship to be given out indefinitely. Assuming an annual interest rate of 5% compounded continuously, do you have enough money to start the scholarship fund?

To determine

Whether the amount of $40,000 is enough or not to start the scholarship fund that is set up by paying an amount P=$18,000 each year at the rate of annual interest as r=5% compounded continuously.

Explanation

Given Information:

An amount of P=$18,000 is paid each year at the rate of annual interest as r=5% compounded continuously and there is an amount of$40,000 to start the fund.

The present value of Perpetuity is given:

Present value=0ertdt=Pr

Where, P is the size of each annual payment and r is the annual interest rate in decimal form.

Write the rate of interest in decimal form as:

r=5%=5100=0

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