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Differential Equation Modeling Question

  1. Feb 19, 2010 #1
    The differential equation dS/dt = kS + D represents the rate of change of savings when S = savings balance, k = interest rate, and D = deposit.

    Ive figured out the solution for the differential equation to be, S = cekt - D/k

    If somebody invest 20,000 each year for the next 40 years with continuous compounded growth of 2%, the final value should be about 1,237,837.

    I dont see how the equation S = cekt - D/k works to 1,237,837.

    I plug c = 20,000, k = .02, t = 40, and D = 20,000 and I get S = -955489

    What am I doing wrong?
  2. jcsd
  3. Feb 19, 2010 #2


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    'c' isn't 20000. The 20000 is D, which is your rate of savings. You have to work out what 'c' is by setting S(0) to be what your initial savings is. It's a boundary value problem.
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