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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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Investment: Rule of 70 Verify that the time necessary for an investment to double in value when compounded continuously is approximately 70/r, where r is the annual interest rate entered as a percent.

To determine

To prove: That the time for an investment to double when compounded continuously is approximately 70r, where, r is the annual interest rate taken as a percent.

Explanation

Given Information:

The provided information is that the investment is compounded continuously and r is the annual interest rate taken as a percent.

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.

Proof:

Consider the exponential growth model A=Pert.

If r is provided as a percentage then the value of r is r100.

Let t be the time for the investment to double, then at time t the accumulated amount A is equal to 2P.

Substitute 2P for A and r100 for r in exponential growth model A=Pert,

2P=Per100t

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