Chapter 4.6, Problem 27E

### Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919

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 27. $750 8 years To determine To calculate: The accumulated amount of an investment of$750 after 10 years and 25 years if it takes 8 years for the investment to double and calculate the annual rate of interest.

Explanation

Given Information:

The provided information is it takes 8 years for the investment to double and the initial investment is $750. 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 8 years for the investment to double and the initial investment is$750.

Here, P=750 and at time t=8, A=2×750=1500.

Substitute t=8, P=750 and A=1500 in the exponential growth model A=Pert,

1500=750er×8e8r=1500750e8r=2

Take natural log on both the sides,

ln(e8r)=ln 28rlne=ln 2r=ln 28

Solve further,

r0.0866

Hence, the annual rate or interest is 8.66%.

Substitute P=750 and r=0

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