anonymous
  • anonymous
eresa invested $1425.00 in a savings account at her local bank. the bank pays simple interest of 3.5% annually. how much money would she have in 4 years?
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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bahrom7893
  • bahrom7893
is this D.E?
bahrom7893
  • bahrom7893
differential equations?
anonymous
  • anonymous
simple interest i guess

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anonymous
  • anonymous
i=prt?
bahrom7893
  • bahrom7893
oh i dunno i never used that stuff
bahrom7893
  • bahrom7893
i think i can do it another way
anonymous
  • anonymous
please show
bahrom7893
  • bahrom7893
okay workin on it, afk
bahrom7893
  • bahrom7893
let me find a similar problem, i was solving these a couple of weeks ago, will get back to u asap
bahrom7893
  • bahrom7893
can u check the answer or do u have the answer?
anonymous
  • anonymous
nopes
bahrom7893
  • bahrom7893
k ill do my best
bahrom7893
  • bahrom7893
So here I am going to use the following differential equation: dN/dt - k*N = 0
bahrom7893
  • bahrom7893
Where N is the amount of money and k is the percent at which it grows. You also know that she invested $1425.00 at some point, so let's call that point the beginning, or time is 0 t = 0
bahrom7893
  • bahrom7893
k is given to be 3.5%; so this is what you know: N(0) = 1425.00 (initial value - initial investment is $1425) dN/dt - 3.5N = 0
bahrom7893
  • bahrom7893
Move -3.5N to the right: dN/dt = 3.5N Multiply both sides by dt: dN = 3.5N*dt Divide both sides by N: dN/n = 3.5dt
bahrom7893
  • bahrom7893
Integrate both sides: \[\int\limits_{}^{}dN/N = \int\limits_{}^{}3.5dt\]
bahrom7893
  • bahrom7893
on the left side you get: ln|N| + C1= 3.5t + C2, where C1 and C2 are arbitrary constants.
bahrom7893
  • bahrom7893
Ln|N| = 3.5t + C2 - C1 (some constant minus another constant is still a constant so ima replace the diff by C3)
bahrom7893
  • bahrom7893
Ln|N| = 3.5t + C3. Now I have to get rid of Ln, so we raise e to the both sides of equation: \[e^{Ln \left| N \right|} = e^{3.5t+C _{3}}\]
bahrom7893
  • bahrom7893
are you following me?
anonymous
  • anonymous
i dont think its that complicated. i am in 6th grade
bahrom7893
  • bahrom7893
okay im sure its not that complicated
bahrom7893
  • bahrom7893
oh well do u want me to finish it? at least get the answer? I think there def is an easier way using logic or smth, but i have no idea how to solve it that way lol. im in college now
anonymous
  • anonymous
:-) thanks for your help. you could try
bahrom7893
  • bahrom7893
wait i think i messed up somewehere in between
bahrom7893
  • bahrom7893
im gettin a ridiculous number
anonymous
  • anonymous
thats ok...i think it would be: Amount= 1425*(3.5/100)*4
bahrom7893
  • bahrom7893
oh crap im using the wrong method. Mine is for changing amount of money, urs is the ez way, they'r assuming that the APR won't change. Like I mean 3.5% of 1425 is not the same as 3.5 of 20k. That's what im solving for, in ur case the 3.5% stays the same.
bahrom7893
  • bahrom7893
which means my solution is totally wrong for this problem lol sorry off to help others, but i really cant do this any other way

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