Chapter 11.2, Problem 43E

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11th Edition

Ronald J. Harshbarger + 1 other

ISBN: 9781305108042

Textbook Problem

** Future value** If

(a) At what rate is the future value growing at any time

(b) At what rate is the future value growing after 1 year *(n* = 1)?

(c) Is the rate of growth of the future value after 1 year greater than 10%? Explain.

**(a)**

To determine

**To calculate:** The rate at which the future value of the *n* if the *n* years and is compounded at 10% interest rate, continuously.

Explanation

**Given Information:**

The future value of the

**Formula used:**

If

According to the property of derivatives, if

According to the power rule of differentiation,

**Calculation:**

Consider the sales function provided,

Differentiate both sides with respect to *n*,

**(b)**

To determine

**To calculate:** The rate at which the future value of the *n* years and is compounded at 10% interest rate, continuously.

**(c)**

To determine

Whether the rate of growth of the future value after 1 year is greater than 10% if the *n* years and is compounded at 10% interest rate, continuously.

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