A young person with no initial capital invests k dollars per year at an annual rate of return r. Assume that investments are made continuously and that the return is compounded continuously. (a) Let S(t) denote the sum of money accumulated from investment after t years, and form an initial value prob- lem that accounts for continuous growth-i.e. that the rate of change is directly proportional to the amount in the amount. (Look at the book if you're not sure what to do here). (b) Determine the sum S(t) accumulated at any time t. (c) If r = 7.5%, determine k so that $1 million will be available for retirement in 40 years. (d) If k= $2000/year, determine the return rate r that must be obtained to have $1 million available in 40 years.

A young person with no initial capital invests k dollars per year at an annual rate of return r. Assume that investments are made continuously and that the return is compounded continuously. (a) Let S(t) denote the sum of money accumulated from investment after t years, and form an initial value prob- lem that accounts for continuous growth-i.e. that the rate of change is directly proportional to the amount in the amount. (Look at the book if you're not sure what to do here). (b) Determine the sum S(t) accumulated at any time t. (c) If r = 7.5%, determine k so that $1 million will be available for retirement in 40 years. (d) If k= $2000/year, determine the return rate r that must be obtained to have $1 million available in 40 years.

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter5: Inverse, Exponential, And Logarithmic Functions

Section5.3: The Natural Exponential Function

Problem 40E

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