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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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Checkpoint 3 Worked-out solution available at LarsonAppliedCalculus.com

Find the annual interest rate for an account whose balance doubles in 8 years and for which the interest is compounded continuously.

To determine

To calculate: The interest rate annually for an account if the balance doubles in 8 years and interest is compounded continuously.

Explanation

Given Information:

The balance doubles in 8 years and interest is compounded continuously.

Formula used:

If the amount P is deposited for t number of years with r rate of interest annually, then the amount A that is compounded continuously is given by

A=Pert

If the expression is in the form of ex=b, then the property of natural logarithms is given by.

lnb=x

Calculation:

Consider the balance in an account, A=Pert.

Here, the amount gets doubled which means A=2P at t=8

Evaluate r by substituting A=2P and t=8 in the equation A=Pert

2P=P

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