   Chapter 4.6, Problem 28E ### 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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# 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 210rlne=ln 2r=ln 210

Solve further,

r0.0693

Hence, the annual rate or interest is 6.93%.

Substitute P=10,000 and r=0

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