   Chapter 4.6, Problem 25E ### 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 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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