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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 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
130. 4% $9000.00

To determine

To calculate: The principal amount that must be invested at the interest rate 4% compounded continuously, so that $9000.00 will be available for retirement 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% and time t=25 for the investment to accumulate to $9000.00.

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% and time t=25 for the investment to accumulate to $9000.00.

Here, r=4% or r=0.04 and at time t=25, A=9000.00.

Let P the initial investment.

Substitute t=25, r=0.04 and A=9000.00 in the exponential growth model A=Pert,

9000.00=Pe0.04×25P=9000.00e0.04×25P=3310.91

Hence, the initial amount is $3310.91.

Let the investment take t time to double, that is, at time t, A=2×3310.91.

Substitute 2×3310.91 for A in the exponential growth model A=3310.91e0.04t,

2×3310

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