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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
25. $1000 12%

To determine

To calculate: The accumulated amount of an investment of $1000 after 10 years and 25 years if the annual rate of interest is 12% and time it will take for the investment to double.

Explanation

Given Information:

The provided information is annual rate of compound interest is 12% and the initial investment is $1000.

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 annual rate of annual interest of 12% and the initial investment is $1000.

Here, r=12% or r=0.12 and P=1000.

Substitute r=0.12 and P=1000 in the exponential growth model A=Pert,

A=1000e0.12t

Let the investment take t time to double, that is, at time t, A=2×1000=2000.

Substitute 2000 for A in the exponential growth model A=1000e0.12t,

2000=1000e0.12te0.12t=20001000e0.12t=2

Take natural log on both the sides,

ln(e0.12t)=ln 20

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