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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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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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