(a) Explanation Given: The differential equation is d S d t = r S and initially the amount deposited is $ 5000 . Procedure used: (1) Form a differential equation. (2)Integrate the differential equation. (3)Apply initial conditions. Calculation: Consider the differential equation. d S d t = r S d S S = r d t (1) Here, the amount is S , the annual rate of interest is r and the time is t . Integrate equation (1). ∫ d S S = ∫ r d t ln S = r t + c S = e r t e c (2) Substitute 5000 for S and 0 for t in equation (2) (b) To determine The time required for the initial amount to be doubled. (c) To determine To Compare: the amount obtained when interest rate is compound quarterly with the amount found in part (a).

6th Edition

ISBN: 9781284105902

Author: Dennis G. Zill

Publisher: Jones & Bartlett Learning

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Question

Chapter 2.7, Problem 10E

(a)

To determine

The amount of money accrued at the end of 5 years.

(b)

To determine

The time required for the initial amount to be doubled.

(c)

To determine

To Compare: the amount obtained when interest rate is compound quarterly with the amount found in part (a).

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Chapter 2.7, Problem 9E

Chapter 2.7, Problem 11E

Chapter 2 Solutions

Advanced Engineering Mathematics

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The amount of money accrued at the end of 5 years .

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The amount of money accrued at the end of 5 years.

The time required for the initial amount to be doubled.

To Compare: the amount obtained when interest rate is compound quarterly with the amount found in part (a).

Want to see the full answer?

Chapter 2 Solutions