   Chapter 4.6, Problem 33E ### 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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# Finding Present Value In Exercises 33 and 34, determine the principal P that must be invested at interest rate r, compounded continuously, so that $1,000,000 will be available for retirement in t years. r = 7.5 % , t = 40 To determine To calculate: The principal amount that must be invested at the interest rate 7.5% compounded continuously, so that$1,000,000 will be available for retirement in 40 years.

Explanation

Given Information:

The provided rate of interest is 7.5% and time t=40 for the investment to accumulate to $1,000,000. 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 rate of interest is 7.5% and time t=40 for the investment to accumulate to$1,000,000.

Here, r=7.5% or r=0.075 and at time t=40, A=1000,000.

Let P the initial investment.

Substitute t=40, r=0

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