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Differential equations

Differential equations

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Differential equations
Your employer automatically puts 10 percent of your salary into a 401(k) retirement account each year. The account earns 4% interest. Suppose you just got the job, your starting salary is $55000, and you expect to receive a 5% raise each year. Additionally, you decide to deposit a fixed amount of $4000 each year to play it conservatively. S'4) = 0.055 For simplicity, assume that interest earned, your raises, and your annual deposit all occur continuously. 0.02 Rt A) Let R(t) denote the dollar value of your retirement account in years. Write the differential equation modeling your account: dR dt B) Solve the differential equation to find R(t), Hint: make use of the Extended Linearity Principle. R(t) = C) Find the value of your retirement account after 35 years. Round answer to 2 decimal places. Value = $
Transcribed Image Text:Your employer automatically puts 10 percent of your salary into a 401(k) retirement account each year. The account earns 4% interest. Suppose you just got the job, your starting salary is $55000, and you expect to receive a 5% raise each year. Additionally, you decide to deposit a fixed amount of $4000 each year to play it conservatively. S'4) = 0.055 For simplicity, assume that interest earned, your raises, and your annual deposit all occur continuously. 0.02 Rt A) Let R(t) denote the dollar value of your retirement account in years. Write the differential equation modeling your account: dR dt B) Solve the differential equation to find R(t), Hint: make use of the Extended Linearity Principle. R(t) = C) Find the value of your retirement account after 35 years. Round answer to 2 decimal places. Value = $
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