Chapter 13.4, Problem 30E

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4th Edition

James Stewart + 2 others

ISBN: 9781305071742

Textbook Problem

**DISCOVER: An Annuity That Lasts Forever **An **annuity in perpetuity **is one that continues forever. Such annuities are useful in setting up scholarship funds to ensure that the award continues.

**(a) **Draw a timeline (as in Example 1) to show that to set up an annuity in perpetuity of amount

where

**(b) **Find the sum of the infinite series in part (a) to show that

**(c) **How much money must be invested now at

**(d) **How much money must be invested now at

To determine

(a)

**To show:**

To set up an annuity in perpetuity of amount

With the help of a timeline, where

Explanation

**Given:**

Timeline for individual payments.

**Approach:**

The amount invested now to set up an annuity in perpetuity

**Calculation:**

Substitute,

For

To determine

(b)

**To show:**

The sum of the infinite series

To determine

(c)

**To find:**

The money that must be invested now at

To determine

(d)

**To find:**

The money that must be invested now at

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