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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 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
30. $2000 $6008.33

To determine

To calculate: The accumulated amount of an investment of $2000 after 10 years if the amount after 25 years is $6008.33 and also calculate the time for the investment to double and the annual rate of interest.

Explanation

Given Information:

The provided information is that the amount after 25 years is $1292.85 and the initial investment is $2000.

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 information that the amount after 25 years is $6008.33 and the initial investment is $2000.

Here, P=$2000 and at time t=25, A=6008.33.

Substitute t=25, P=$2000 and A=6008.33 in the exponential growth model A=Pert,

6008.33=2000er×25e25r=6008.332000

Take natural log on both the sides,

ln(e25r)=ln (6008.332000)25rlne=ln (1292.85500)r=ln (6008.332000)25r0.044

Hence, the annual rate or interest is 4.4%.

Substitute P=$2000 and r=0.044 in the exponential growth model A=Pert,

A=2000e0

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