   Chapter 4.6, Problem 31E ### 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. InitialInvestment rate Annual Time to Amountafter Amountafter double 10 years 25 years 31. 4.5% $15,000.00 To determine To calculate: The principal amount that must be invested at the interest rate 4.5% compounded continuously, so that$15,000.00 will be available in 25 years, also calculate the time it will take for the investment to double and the accumulated amount after 10 years.

Explanation

Given Information:

The provided rate of interest is 4.5% and amount after 25 years is $15,000.00. 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 rate of interest is 4.5% and time t=25 for the investment to accumulate to$15,000.00.

Here, r=4.5% or r=0.045 and at time t=25, A=15,000.00.

Let P the initial investment.

Substitute t=25,r=0.045 and A=15,000.00 in the exponential growth model A=Pert,

15,000.00=Pe0.045×25P=15,000.00e0.045×25P=4869.79

Hence, the initial amount is \$4869.79.

Let the investment take t time to double, that is, at time t A=2×4869.79.

Substitute 2×4869.79 for A in the exponential growth model A=4869.79e0

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