Chapter 12.5, Problem 40E

### Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042

Chapter
Section

### Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042
Textbook Problem

# Compound interest In Problems 39 and 40, use the following information.When interest is compounded continuously, the rate of change of the amount x of the investment is proportional to the amount present. In this case, the proportionality constant is the annual interest rate r (as a decimal); that is, d x d t = r x (a) If $2000 is invested at 8 % compounded continuously, find an equation for the future value of the investment as a function of time t, in years.(b) How long will it take for the investment to double?(c) What will be the future value of this investment after 35 years? (a) To determine To calculate: The equation for the future value of the investment as a function of time t in years dxdt=rx and$2,000 is invested at 8% compounded continuously.

Explanation

Given Information:

If $2,000 is invested at 8% compounded continuously. The interest is compounded continuously, the rate of change of the amount x of the investment is proportional to the amount present. The proportional constant is the annual interest rate r as: dxdt=rx Formula used: The differential equation can be equivalently expressed in the form g(y)dy=f(x)dx. Then the equation is separable. The solution of a separable differential is obtained by integrating both sides of the equation after the variable have been separated. Calculation: The interest is compounded continuously, the rate of change of the amount x of the investment is proportional to the amount present. The proportional constant is the annual interest rate r as: dxdt=rx If$10,000 is invested at 6% compounded continuously is r=0

(c)

To determine

To calculate: The time required to double the future value of investment.

(c)

To determine

To calculate: the future value of the investment after 35 years.

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