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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 127-130, complete the table for an account in which interest is compounded continuously.

Initialinvestment Annualrate Time to double Amount after 10 years Amount after 25 years
128. $2000 7 years

To determine

To calculate: The accumulated amount of an investment of $2000 after 10 years and 25 years if it takes 7 years for the investment to double and calculate the annual rate of interest.

Explanation

Given Information:

The provided information is it takes 7 years for the investment to double and the initial investment is $2000.

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 7 years for the investment to double and the initial investment is $2000.

Here, P=2000 and at time t=7, A=2×2000=4000

Substitute t=7, P=2000 and A=4000 in the exponential growth model A=Pert,

4000=2000er×7e7r=20004000e7r=2

Take natural log on both the sides,

ln(e7r)=ln 27rlne=ln 2r=ln 27r0.0990

Hence, the annual rate or interest is 9.90%.

Substitute P=2000 and r=0

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