   Chapter 4.4, Problem 76E ### 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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# Compound Interest Complete the table to determine the time t necessary for P dollars to triple when the interest is compounded continuously at rate r. r 2% 4% 6% 8% 10% 12% 14% t

To determine

To calculate: The time required t (in years) so that the deposited amount P (in dollars) become triple for the corresponding values of rate r that is, compounded continuously in the following table:

 r 2% 4% 6% 8% 10% 12% 14% t
Explanation

Given Information:

The deposited amount P (in dollars) become triple when the interest is compounded continuously and the table is as follows:

 r 2% 4% 6% 8% 10% 12% 14% t

Formula used:

The balance amount after t years when interest at i is compounded continuously is,

A=Pert

Where, P is the deposited amount, A is the amount after t years, r is the interest rate in decimals and t is the number of years.

The inverse property of logarithms for the expression lnex is lnex=x.

Calculation:

Consider that the deposited amount P (in dollars) become triple when the interest is compounded continuously

Now, the amount will become triple of the deposited amount after t years, then the amount after t years is 3P, that is,

A=3P.

Substitute Pert for A.

3P=Pert

Divide both sides by P as,

3PP=PertPert=3

Take natural logarithm on both sides as,

ln(ert)=ln3

Now, apply the inverse property of lnex as,

rt=ln3

Divide both sides by r as,

rtr=ln3rt=ln3r

When r=2%,

The interest rate is,

r=2%=2100=0.02

Compute the time required when the interest rate is 2%.

Substitute 0.02 for r in t=ln3r.

t=ln30.021.09860.0254.93 years

When r=4%,

The interest rate is,

r=4%=4100=0.04

Compute the time required when the interest rate is 4%.

Substitute 0.04 for r in t=ln3r.

t=ln30.041.09860.0427.47 years

When r=6%,

The interest rate is,

r=6%=6100=0.06

Compute the time required when the interest rate is 6%

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