   Chapter 4.6, Problem 38E ### 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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# Investment: Rule of 70 Use the Rule of 70 from Exercise 37 to approximate the times necessary for an investment to double in value when compounded continuously for (a) r =   10 % and (b) r =   7 % .

(a)

To determine

To calculate: The time required for an investment to double compound continuously at annual rate of interest r=10% using the rule of 70.

Explanation

Given Information:

The provided annual rate of interest is 10%.

Formula used:

The accumulated amount for an initial investment P compounded continuously at an annual rate of interest r is given by the exponential growth model A=Pert.

Rule of 70:

The time for an investment to double when compounded continuously is approximately 70r, where, r is the annual interest rate entered as a percent.

Calculation:

Consider the annual rate of interest r=10%.

Consider the exponential growth model A=Pert.

If r is provided as a percentage then the value of r is r100.

Let t be the time for the investment to double, then at time t the accumulated amount A is equal to 2P.

Substitute 2P for A and r100 for r in exponential growth model A=Pert,

2P=Per100t2=er

(b)

To determine

To calculate: The time required for an investment to double compound continuously at annual rate of interest r=7% using the rule of 70.

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