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

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Chapter 4.4, Problem 75E
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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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Compound Interest A deposit of $1000 is made in an account that earns interest at an annual rate of 5%. How long will it take for the balance to double when the interest is compounded (a) annually, (b) monthly, (c) daily, and (d) continuously?

(a)

To determine

To calculate: The time required so that the deposited amount become double if the amount of $1000 is deposited in an account at the interest rate of 5% and the interest is compounded annually.

Explanation

Given Information:

The amount of $1000 is deposited in an account at the interest rate of 5% and the interest is compounded annually.

Formula used:

The compound interest formula,

A=P(1+rn)nt

Where, P is the deposited amount, A is the amount after t years, r is the interest rate in decimals, t is the number of years and n is the number of times compounded per year.

The property of logarithms for the expression lnxn is lnxn=nlnx where x and y are real numbers greater than 0.

Calculation:

Consider that the amount of $1000 is deposited in an account at the interest rate of 5% and the interest is compounded annually.

Since, the principal amount deposit in the account is $1000 at interest rate of

P=$1000, r=5%.

The number of times compounded per year is 1 as the interest is compounded annually, that is,

n=1.

Now, the amount become double of the deposited amount after t years, then the amount after t years is 2P, that is,

A=2P=2($1000)=$2000

The rate of interest compounded annually is,

r=5%=5100=0.05

Substitute 0.05 for i, $1000 for P, 1 for n, and $2000 for A in A=P(1+rn)nt

(b)

To determine

To calculate: The time required so that the deposited amount become double if the amount of $1000 is deposited in an account at the interest rate of 5% and the interest is compounded monthly.

(c)

To determine

To calculate: The time required so that the deposited amount become double if the amount of $1000 is deposited in an account at the interest rate of 5% and the interest is compounded daily.

(d)

To determine

To calculate: The time required so that the deposited amount become double if the amount of $1000 is deposited in an account at the interest rate of 5% and the interest is compounded continuously.

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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 P-13ESect-4.2 P-14ESect-4.2 P-15ESect-4.2 P-16ESect-4.2 P-17ESect-4.2 P-18ESect-4.2 P-19ESect-4.2 P-20ESect-4.2 P-21ESect-4.2 P-22ESect-4.2 P-23ESect-4.2 P-24ESect-4.2 P-25ESect-4.2 P-26ESect-4.2 P-27ESect-4.2 P-28ESect-4.2 P-29ESect-4.2 P-30ESect-4.2 P-31ESect-4.2 P-32ESect-4.2 P-33ESect-4.2 P-34ESect-4.2 P-35ESect-4.2 P-36ESect-4.2 P-37ESect-4.2 P-38ESect-4.2 P-39ESect-4.2 P-40ESect-4.2 P-41ESect-4.2 P-42ESect-4.2 P-43ESect-4.2 P-44ESect-4.2 P-45ESect-4.2 P-46ESect-4.2 P-47ESect-4.2 P-48ESect-4.2 P-49ESect-4.2 P-50ESect-4.2 P-51ESect-4.3 P-1CPSect-4.3 P-2CPSect-4.3 P-3CPSect-4.3 P-4CPSect-4.3 P-5CPSect-4.3 P-6CPSect-4.3 P-1SWUSect-4.3 P-2SWUSect-4.3 P-3SWUSect-4.3 P-4SWUSect-4.3 P-5SWUSect-4.3 P-6SWUSect-4.3 P-7SWUSect-4.3 P-8SWUSect-4.3 P-9SWUSect-4.3 P-10SWUSect-4.3 P-1ESect-4.3 P-2ESect-4.3 P-3ESect-4.3 P-4ESect-4.3 P-5ESect-4.3 P-6ESect-4.3 P-7ESect-4.3 P-8ESect-4.3 P-9ESect-4.3 P-10ESect-4.3 P-11ESect-4.3 P-12ESect-4.3 P-13ESect-4.3 P-14ESect-4.3 P-15ESect-4.3 P-16ESect-4.3 P-17ESect-4.3 P-18ESect-4.3 P-19ESect-4.3 P-20ESect-4.3 P-21ESect-4.3 P-22ESect-4.3 P-23ESect-4.3 P-24ESect-4.3 P-25ESect-4.3 P-26ESect-4.3 P-27ESect-4.3 P-28ESect-4.3 P-29ESect-4.3 P-30ESect-4.3 P-31ESect-4.3 P-32ESect-4.3 P-33ESect-4.3 P-34ESect-4.3 P-35ESect-4.3 P-36ESect-4.3 P-37ESect-4.3 P-38ESect-4.3 P-39ESect-4.3 P-40ESect-4.3 P-41ESect-4.3 P-42ESect-4.3 P-43ESect-4.3 P-44ESect-4.3 P-45ESect-4.3 P-46ESect-4.3 P-47ESect-4.3 P-48ESect-4.3 P-49ESect-4.3 P-50ESect-4.3 P-51ESect-4.3 P-52ESect-4.3 P-53ESect-4.3 P-1QYSect-4.3 P-2QYSect-4.3 P-3QYSect-4.3 P-4QYSect-4.3 P-5QYSect-4.3 P-6QYSect-4.3 P-7QYSect-4.3 P-8QYSect-4.3 P-9QYSect-4.3 P-10QYSect-4.3 P-11QYSect-4.3 P-12QYSect-4.3 P-13QYSect-4.3 P-14QYSect-4.3 P-15QYSect-4.3 P-16QYSect-4.3 P-17QYSect-4.3 P-18QYSect-4.3 P-19QYSect-4.3 P-20QYSect-4.3 P-21QYSect-4.3 P-22QYSect-4.3 P-23QYSect-4.3 P-24QYSect-4.3 P-25QYSect-4.4 P-1CPSect-4.4 P-2CPSect-4.4 P-3CPSect-4.4 P-4CPSect-4.4 P-5CPSect-4.4 P-6CPSect-4.4 P-7CPSect-4.4 P-1SWUSect-4.4 P-2SWUSect-4.4 P-3SWUSect-4.4 P-4SWUSect-4.4 P-5SWUSect-4.4 P-6SWUSect-4.4 P-7SWUSect-4.4 P-8SWUSect-4.4 P-9SWUSect-4.4 P-10SWUSect-4.4 P-1ESect-4.4 P-2ESect-4.4 P-3ESect-4.4 P-4ESect-4.4 P-5ESect-4.4 P-6ESect-4.4 P-7ESect-4.4 P-8ESect-4.4 P-9ESect-4.4 P-10ESect-4.4 P-11ESect-4.4 P-12ESect-4.4 P-13ESect-4.4 P-14ESect-4.4 P-15ESect-4.4 P-16ESect-4.4 P-17ESect-4.4 P-18ESect-4.4 P-19ESect-4.4 P-20ESect-4.4 P-21ESect-4.4 P-22ESect-4.4 P-23ESect-4.4 P-24ESect-4.4 P-25ESect-4.4 P-26ESect-4.4 P-27ESect-4.4 P-28ESect-4.4 P-29ESect-4.4 P-30ESect-4.4 P-31ESect-4.4 P-32ESect-4.4 P-33ESect-4.4 P-34ESect-4.4 P-35ESect-4.4 P-36ESect-4.4 P-37ESect-4.4 P-38ESect-4.4 P-39ESect-4.4 P-40ESect-4.4 P-41ESect-4.4 P-42ESect-4.4 P-43ESect-4.4 P-44ESect-4.4 P-45ESect-4.4 P-46ESect-4.4 P-47ESect-4.4 P-48ESect-4.4 P-49ESect-4.4 P-50ESect-4.4 P-51ESect-4.4 P-52ESect-4.4 P-53ESect-4.4 P-54ESect-4.4 P-55ESect-4.4 P-56ESect-4.4 P-57ESect-4.4 P-58ESect-4.4 P-59ESect-4.4 P-60ESect-4.4 P-61ESect-4.4 P-62ESect-4.4 P-63ESect-4.4 P-64ESect-4.4 P-65ESect-4.4 P-66ESect-4.4 P-67ESect-4.4 P-68ESect-4.4 P-69ESect-4.4 P-70ESect-4.4 P-71ESect-4.4 P-72ESect-4.4 P-73ESect-4.4 P-74ESect-4.4 P-75ESect-4.4 P-76ESect-4.4 P-77ESect-4.4 P-78ESect-4.4 P-79ESect-4.4 P-80ESect-4.4 P-81ESect-4.4 P-82ESect-4.4 P-83ESect-4.4 P-84ESect-4.4 P-85ESect-4.4 P-86ESect-4.4 P-87ESect-4.4 P-88ESect-4.4 P-89ESect-4.4 P-90ESect-4.4 P-91ESect-4.4 P-92ESect-4.4 P-93ESect-4.4 P-94ESect-4.4 P-95ESect-4.4 P-96ESect-4.4 P-97ESect-4.4 P-98ESect-4.5 P-1CPSect-4.5 P-2CPSect-4.5 P-3CPSect-4.5 P-4CPSect-4.5 P-5CPSect-4.5 P-6CPSect-4.5 P-7CPSect-4.5 P-8CPSect-4.5 P-9CPSect-4.5 P-10CPSect-4.5 P-1SWUSect-4.5 P-2SWUSect-4.5 P-3SWUSect-4.5 P-4SWUSect-4.5 P-5SWUSect-4.5 P-6SWUSect-4.5 P-7SWUSect-4.5 P-8SWUSect-4.5 P-9SWUSect-4.5 P-10SWUSect-4.5 P-1ESect-4.5 P-2ESect-4.5 P-3ESect-4.5 P-4ESect-4.5 P-5ESect-4.5 P-6ESect-4.5 P-7ESect-4.5 P-8ESect-4.5 P-9ESect-4.5 P-10ESect-4.5 P-11ESect-4.5 P-12ESect-4.5 P-13ESect-4.5 P-14ESect-4.5 P-15ESect-4.5 P-16ESect-4.5 P-17ESect-4.5 P-18ESect-4.5 P-19ESect-4.5 P-20ESect-4.5 P-21ESect-4.5 P-22ESect-4.5 P-23ESect-4.5 P-24ESect-4.5 P-25ESect-4.5 P-26ESect-4.5 P-27ESect-4.5 P-28ESect-4.5 P-29ESect-4.5 P-30ESect-4.5 P-31ESect-4.5 P-32ESect-4.5 P-33ESect-4.5 P-34ESect-4.5 P-35ESect-4.5 P-36ESect-4.5 P-37ESect-4.5 P-38ESect-4.5 P-39ESect-4.5 P-40ESect-4.5 P-41ESect-4.5 P-42ESect-4.5 P-43ESect-4.5 P-44ESect-4.5 P-45ESect-4.5 P-46ESect-4.5 P-47ESect-4.5 P-48ESect-4.5 P-49ESect-4.5 P-50ESect-4.5 P-51ESect-4.5 P-52ESect-4.5 P-53ESect-4.5 P-54ESect-4.5 P-55ESect-4.5 P-56ESect-4.5 P-57ESect-4.5 P-58ESect-4.5 P-59ESect-4.5 P-60ESect-4.5 P-61ESect-4.5 P-62ESect-4.5 P-63ESect-4.5 P-64ESect-4.5 P-65ESect-4.5 P-66ESect-4.5 P-67ESect-4.5 P-68ESect-4.5 P-69ESect-4.5 P-70ESect-4.5 P-71ESect-4.5 P-72ESect-4.5 P-73ESect-4.5 P-74ESect-4.5 P-75ESect-4.5 P-76ESect-4.5 P-77ESect-4.5 P-78ESect-4.5 P-79ESect-4.5 P-80ESect-4.5 P-81ESect-4.5 P-82ESect-4.5 P-83ESect-4.6 P-1CPSect-4.6 P-2CPSect-4.6 P-3CPSect-4.6 P-4CPSect-4.6 P-1SWUSect-4.6 P-2SWUSect-4.6 P-3SWUSect-4.6 P-4SWUSect-4.6 P-5SWUSect-4.6 P-6SWUSect-4.6 P-7SWUSect-4.6 P-8SWUSect-4.6 P-9SWUSect-4.6 P-10SWUSect-4.6 P-11SWUSect-4.6 P-12SWUSect-4.6 P-1ESect-4.6 P-2ESect-4.6 P-3ESect-4.6 P-4ESect-4.6 P-5ESect-4.6 P-6ESect-4.6 P-7ESect-4.6 P-8ESect-4.6 P-9ESect-4.6 P-10ESect-4.6 P-11ESect-4.6 P-12ESect-4.6 P-13ESect-4.6 P-14ESect-4.6 P-15ESect-4.6 P-16ESect-4.6 P-17ESect-4.6 P-18ESect-4.6 P-19ESect-4.6 P-20ESect-4.6 P-21ESect-4.6 P-22ESect-4.6 P-23ESect-4.6 P-24ESect-4.6 P-25ESect-4.6 P-26ESect-4.6 P-27ESect-4.6 P-28ESect-4.6 P-29ESect-4.6 P-30ESect-4.6 P-31ESect-4.6 P-32ESect-4.6 P-33ESect-4.6 P-34ESect-4.6 P-35ESect-4.6 P-36ESect-4.6 P-37ESect-4.6 P-38ESect-4.6 P-39ESect-4.6 P-40ESect-4.6 P-41ESect-4.6 P-42ESect-4.6 P-43ESect-4.6 P-44ESect-4.6 P-45ESect-4.6 P-46ECh-4 P-1RECh-4 P-2RECh-4 P-3RECh-4 P-4RECh-4 P-5RECh-4 P-6RECh-4 P-7RECh-4 P-8RECh-4 P-9RECh-4 P-10RECh-4 P-11RECh-4 P-12RECh-4 P-13RECh-4 P-14RECh-4 P-15RECh-4 P-16RECh-4 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P-107RECh-4 P-108RECh-4 P-109RECh-4 P-110RECh-4 P-111RECh-4 P-112RECh-4 P-113RECh-4 P-114RECh-4 P-115RECh-4 P-116RECh-4 P-117RECh-4 P-118RECh-4 P-119RECh-4 P-120RECh-4 P-121RECh-4 P-122RECh-4 P-123RECh-4 P-124RECh-4 P-125RECh-4 P-126RECh-4 P-127RECh-4 P-128RECh-4 P-129RECh-4 P-130RECh-4 P-131RECh-4 P-132RECh-4 P-1TYSCh-4 P-2TYSCh-4 P-3TYSCh-4 P-4TYSCh-4 P-5TYSCh-4 P-6TYSCh-4 P-7TYSCh-4 P-8TYSCh-4 P-9TYSCh-4 P-10TYSCh-4 P-11TYSCh-4 P-12TYSCh-4 P-13TYSCh-4 P-14TYSCh-4 P-15TYSCh-4 P-16TYSCh-4 P-17TYSCh-4 P-18TYSCh-4 P-19TYSCh-4 P-20TYSCh-4 P-21TYSCh-4 P-22TYSCh-4 P-23TYSCh-4 P-24TYSCh-4 P-25TYSCh-4 P-26TYSCh-4 P-27TYSCh-4 P-28TYSCh-4 P-29TYS

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Calculus: Early Transcendental Functions (MindTap Course List)

Analyzing a Graph Consider the function f(x)=21+e1/x (a) Use a graphing utility to graph f. (b) Write a short p...

Calculus of a Single Variable

Figure MNPQ is a rhombus. Draw diagonals MP and QN of the rhombus. How do MP and QN appear to be related?

Elementary Geometry for College Students

Let A=[abcd] a.Find A1 if it exists. b.Find a necessary condition for A to be nonsingular. c.Verify that AA1=A1...

Finite Mathematics for the Managerial, Life, and Social Sciences

Finding a Derivative of a Trigonometric Function In Exercises 41-56. find the derivative of the trigonometric f...

Calculus

Removable and Nonremovable Discontinuities In Exercises 5358, find the x-values (if any) at which f is not cont...

Calculus (MindTap Course List)

Evaluating a Surface Integral In Exercises 19-24, evaluate sf(x,y,z)dS f(x,y,z)=xyzS:z=x2+y2,4x2+y216

Multivariable Calculus

Given the Taylor Series , a Taylor series for ex/2 is:

Study Guide for Stewart's Multivariable Calculus, 8th

f(x)=2x2+1x+3 has slant asymptote(s): a) y = 2x b) y = x c) y = 2x and y = 2x d) f does not have slant asymptot...

Study Guide for Stewart's Single Variable Calculus: Early Transcendentals, 8th

Critical Thinking: Determine if the statement is true or false. If the statement is false, then correct it and ...

College Algebra (MindTap Course List)

Two fuel additives are tested to determine their effect on miles per gallon for passenger cars. Test results fo...

Statistics for Business & Economics, Revised (MindTap Course List)

For Exercises 27 through 30, compute the required angle using this formula: tanC=tanAcosB Given: A=3400 B=800 C...

Mathematics For Machine Technology

An automobile dealer reports the Year 1 and Year 8 sales for three models in the following table. Compute quant...

STATISTICS F/BUSINESS+ECONOMICS-TEXT

Describe how between-subjects designs are used to compare means and proportions for two or more groups, identif...

Research Methods for the Behavioral Sciences (MindTap Course List)

An article from the Associated Press (May 14, 2002) led with the headline Academic Success Lowers Pregnancy Ris...

Introduction To Statistics And Data Analysis

How does a multiple-baseline design rule out chance or coincidence as the explanation for changes in behavior t...

Research Methods for the Behavioral Sciences (MindTap Course List)

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