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FO Differential equations and account balanceby fogvajarash
Tags: account, balance, calculus, differential, equations, interest, variables separable 
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#1
Oct2713, 10:15 PM

P: 126

1. The problem statement, all variables and given/known data
a. Assume that y_{o} dollars are deposited into an account paying r percent compounded continuously. If withdrawals are at an annual rate of 200t dollars (assume these are continuous), find the amount in the account after T years. b. Consider the special case if r = 10% and y_{0}=$20000 c. When will the account be depleted if y_{0}=$5000? Give your answer to the nearest month. 2. Relevant equations 3. The attempt at a solution I've realized that the rate at which the account balance varies is the following: dy/dt = ry  200 (where r is the r percent rate, 0.10; and y the amount of money present) However, when i try to obtain the differential equation, I keep getting that the amount of money present is the following: y(T) = 200/r + (y_{0}200/r)e^{rT} This would, mean that the function would never decrease in the case of $20000 and as well for $5000 (meaning it will never be depleted). However, I'm pretty sure that i'm wrong on this one. Could anyone please help me with this? My procedure: 1/(ry200) dy = 1 dt (integrate both parts) ln(ry200) 1/r = t + M_{1} ln(ry200) = rt + M_{2} M_{3}e^{rt}=ry200 y = M_{4}e^{rt} + 200/r Then, if y(0) = y_{0}: y_{0}  200/r = M_{4} We then plug this result into our equation: y = 200/r + (y_{0}  200/r)e^{rT} This corresponds to the equation i've been getting. Is my procedure done right? 


#2
Oct2713, 10:36 PM

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P: 5,187

In the corrected problem the value of y0 determines whether or not the account will ever be depleted, and when that will happen. 


#3
Oct2813, 06:46 AM

P: 126




#4
Oct2813, 09:31 AM

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P: 5,370

FO Differential equations and account balance
Chet 


#5
Oct2813, 09:50 AM

Sci Advisor
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P: 5,187

u



#6
Oct2913, 12:07 AM

P: 126




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