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Homework Help: Differential equations interest probelm

  1. Nov 26, 2012 #1
    1. The problem statement, all variables and given/known data
    Two same aged people P1,P2 create bank accounts at ages 25,35 respectively, and add 2000 euros annualy , for 10,30 years respectively. No initial capital in the accounts.

    1.For interest 8% , what's the balance of each acount at age of 65 of P1,P2?
    2.What should be the interest for the above balances to be equal

    3. The attempt at a solution
    I guess continuous interest is assumed.

    The problem here is the constant 2000/year.
    The interest r affects the balance in the form of
    [tex]S_r(t) = S_0e^{rt}[/tex] , while the constant deposits [tex] S_{c0}(t) = S_{c0} + 2000t [/tex]

    edit : To the result of the bank's interest over a year, 2000 is added and the total is considered the balance for the application of interest at the next year.
    Does it hold to say:
    [tex] \frac{dS}{dt} = (2000+S)r \iff S(t) = S_0 e^{rt} + 2000rt[/tex] ?

    Do i have to combine them somehow / write the relation as a DE and find the solution?
    Last edited: Nov 26, 2012
  2. jcsd
  3. Nov 26, 2012 #2
    I think i got it:
    S(t) = e^{rt}+2000rt+2000t
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