Chapter 4, Problem 127RE

### Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919

Chapter
Section

### 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 127. $600 8% To determine To calculate: The accumulated amount of an investment of$600 after 10 years and 25 years if the annual rate of interest is 8% and time it will take for the investment to double.

Explanation

Given Information:

The provided information is annual rate of compound interest is 8% and the initial investment is $600. 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 8% and the initial investment is$600.

Here, r=8% or r=0.08 and P=600.

Substitute r=0.08 and P=600 in the exponential growth model A=Pert,

A=600e0.08t

Let the investment take t time to double, that is, at time t, A=2×600=1200.

Substitute 1200 for A in the exponential growth model A=600e0.08t,

1200=600e0.08te0.08t=1200600e0.08t=2

Take natural log on both the sides,

ln(e0.08t)=ln 20

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