Chapter 4.6, Problem 29E

### 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 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 29. $500$1292.85

To determine

To calculate: The accumulated amount of an investment of $500 after 25 years if the amount after 10 years is$1292.85 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 10 years is $1292.85 and the initial investment is$500.

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 10 years is $1292.85 and the initial investment is$500.

Here, P=$500 and at time t=10, A=1292.85. Substitute t=10, P=$500 and A=1292.85 in the exponential growth model A=Pert,

1292.85=500er×10e10r=1292.85500

Take natural log on both the sides,

ln(e10r)=ln (1292.85500)10rlne=ln (1292.85500)r=ln (1292.85500)10r0.095

Hence, the annual rate or interest is 9.5%.

Substitute P=500 and r=0.095 in the exponential growth model A=Pert,

A=500e0

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