   Chapter 4.6, Problem 26E ### 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 26. $20,000 10 1 2 % To determine To calculate: The accumulated amount of an investment of$20,000 after 10 years and 25 years if the annual rate of interest is 1012% and time it will take for the investment to double.

Explanation

Given Information:

The provided information is annual rate of compound interest is 1012% and the initial investment is $20,000. 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$20,000.

Here, r=1012% or r=0.105 and P=20,000.

Substitute r=0.105 and P=20,000 in the exponential growth model A=Pert,

A=20000e0.105t

Let the investment take t time to double, that is, at time t, A=2×20000=40000.

Substitute 40000 for A in the exponential growth model A=20000e0.105t,

40000=20000e0.105te0.105t=4000020000e0.105t=2

Take natural log on both the sides,

ln(e0.105t)=ln 20

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