Chapter 4, Problem 20TYS

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10th Edition

Ron Larson

ISBN: 9781305860919

Textbook Problem

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A deposit of $500 is made in an account that earns interest at an annual rate of 4%. 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 will become double if the amount of

Explanation

**Given Information:**

The amount of

**Formula used:**

The formula to compute the balance amount after *t* years when interest is compounded *n* times per year is,

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 *x* and *y* are real numbers greater than

**Calculation:**

Consider that the amount of

Here,

The number of times compounded per year is

As the amount will become double of the deposited amount after *t* years, then the amount after *t* years is

Simplify the rate as,

Substitute *t* years in the formula,

**(b)**

To determine

**To calculate:** The time required so that the deposited amount will become double if the amount of

**(c)**

To determine

**To calculate:** The time required so that the deposited amount will become double if the amount of

**(d)**

To determine

**To calculate:** The time required so that the deposited amount will become double if the amount of

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 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P-17RECh-4 P-18RECh-4 P-19RECh-4 P-20RECh-4 P-21RECh-4 P-22RECh-4 P-23RECh-4 P-24RECh-4 P-25RECh-4 P-26RECh-4 P-27RECh-4 P-28RECh-4 P-29RECh-4 P-30RECh-4 P-31RECh-4 P-32RECh-4 P-33RECh-4 P-34RECh-4 P-35RECh-4 P-36RECh-4 P-37RECh-4 P-38RECh-4 P-39RECh-4 P-40RECh-4 P-41RECh-4 P-42RECh-4 P-43RECh-4 P-44RECh-4 P-45RECh-4 P-46RECh-4 P-47RECh-4 P-48RECh-4 P-49RECh-4 P-50RECh-4 P-51RECh-4 P-52RECh-4 P-53RECh-4 P-54RECh-4 P-55RECh-4 P-56RECh-4 P-57RECh-4 P-58RECh-4 P-59RECh-4 P-60RECh-4 P-61RECh-4 P-62RECh-4 P-63RECh-4 P-64RECh-4 P-65RECh-4 P-66RECh-4 P-67RECh-4 P-68RECh-4 P-69RECh-4 P-70RECh-4 P-71RECh-4 P-72RECh-4 P-73RECh-4 P-74RECh-4 P-75RECh-4 P-76RECh-4 P-77RECh-4 P-78RECh-4 P-79RECh-4 P-80RECh-4 P-81RECh-4 P-82RECh-4 P-83RECh-4 P-84RECh-4 P-85RECh-4 P-86RECh-4 P-87RECh-4 P-88RECh-4 P-89RECh-4 P-90RECh-4 P-91RECh-4 P-92RECh-4 P-93RECh-4 P-94RECh-4 P-95RECh-4 P-96RECh-4 P-97RECh-4 P-98RECh-4 P-99RECh-4 P-100RECh-4 P-101RECh-4 P-102RECh-4 P-103RECh-4 P-104RECh-4 P-105RECh-4 P-106RECh-4 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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