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CalculusCalculus: An Applied Approach (MindTap Course List)10th Edition

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Chapter 4.6, Problem 28E
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Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919

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Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919
Textbook Problem
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Modeling Compound Interest In Exercises 25-32, complete the table for an account in which interest is compounded continuously.

See Example 3.

Amount after 10 years Amount after 25 years
Initial Annual Time to double
investment rate
28. $10,000 10 years

To determine

To calculate: The accumulated amount of an investment of $10,000 after 10 years and 25 years if it takes 10 years for the investment to double and calculate the annual rate of interest.

Explanation

Given Information:

The provided information is it takes 10 years for the investment to double and the initial investment is $10,000.

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.

Calculation:

Consider the provided information that it takes 10 years for the investment to double and the initial investment is $10,000.

Here, P=10,000 and at time t=10, A=2×10,000=20,000.

Substitute t=10, P=10,000 and A=20,000 in the exponential growth model A=Pert,

20,000=10,000er×10e10r=20,00010,000e10r=2

Take natural log on both the sides,

ln(e10r)=ln 210r⋅lne=ln 2r=ln 210

Solve further,

r≈0.0693

Hence, the annual rate or interest is 6.93%.

Substitute P=10,000 and r=0

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Sect-4.1 P-1CPSect-4.1 P-2CPSect-4.1 P-3CPSect-4.1 P-4CPSect-4.1 P-5CPSect-4.1 P-1SWUSect-4.1 P-2SWUSect-4.1 P-3SWUSect-4.1 P-4SWUSect-4.1 P-5SWU
Sect-4.1 P-6SWUSect-4.1 P-7SWUSect-4.1 P-8SWUSect-4.1 P-9SWUSect-4.1 P-10SWUSect-4.1 P-11SWUSect-4.1 P-12SWUSect-4.1 P-13SWUSect-4.1 P-14SWUSect-4.1 P-15SWUSect-4.1 P-16SWUSect-4.1 P-17SWUSect-4.1 P-18SWUSect-4.1 P-1ESect-4.1 P-2ESect-4.1 P-3ESect-4.1 P-4ESect-4.1 P-5ESect-4.1 P-6ESect-4.1 P-7ESect-4.1 P-8ESect-4.1 P-9ESect-4.1 P-10ESect-4.1 P-11ESect-4.1 P-12ESect-4.1 P-13ESect-4.1 P-14ESect-4.1 P-15ESect-4.1 P-16ESect-4.1 P-17ESect-4.1 P-18ESect-4.1 P-19ESect-4.1 P-20ESect-4.1 P-21ESect-4.1 P-22ESect-4.1 P-23ESect-4.1 P-24ESect-4.1 P-25ESect-4.1 P-26ESect-4.1 P-27ESect-4.2 P-1CPSect-4.2 P-2CPSect-4.2 P-3CPSect-4.2 P-4CPSect-4.2 P-5CPSect-4.2 P-1SWUSect-4.2 P-2SWUSect-4.2 P-3SWUSect-4.2 P-4SWUSect-4.2 P-5SWUSect-4.2 P-6SWUSect-4.2 P-7SWUSect-4.2 P-8SWUSect-4.2 P-9SWUSect-4.2 P-10SWUSect-4.2 P-11SWUSect-4.2 P-12SWUSect-4.2 P-1ESect-4.2 P-2ESect-4.2 P-3ESect-4.2 P-4ESect-4.2 P-5ESect-4.2 P-6ESect-4.2 P-7ESect-4.2 P-8ESect-4.2 P-9ESect-4.2 P-10ESect-4.2 P-11ESect-4.2 P-12ESect-4.2 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Statistics for Business & Economics, Revised (MindTap Course List)

Describe the four methods for administering a survey (mail, phone, Internet, and in person) and explain the str...

Research Methods for the Behavioral Sciences (MindTap Course List)

Choosing a Formula In Exercises 514, select the basic integration formula you can use to find the indefinite in...

Calculus (MindTap Course List)

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