1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Annuity differential equation

Tags:
  1. Sep 25, 2007 #1
    I'm trying to figure out the solution to a differential equation that describes the accrued interest on an annuity - rather than a lump sum at the beginning, we're dealing with multiple and regular deposits. The prof implied that we would have to solve for the dif eq'n
    S' = k + rS
    where k is the deposit, r the interest rate and S(t) the amount of money accrued at time t. I think I've solved for this particular equation (with intinial condition S(0) - So) which is
    S(t) = (So + k)e^rt - k
    but I have two questions. First, this doesn't seem right in terms of the fact that I'm subtracting k at the end there. And secondly, should k somehow be in terms of t as well (i.e. k(t) since the deposits are regular, i.e. at time t, I will have made k(t) deposits?)

    Any insight would be appreicated...

    Thanks,
    W.
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Sep 25, 2007 #2

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    Look what happens when t= 0. e^0= 1 so S(0)= S0+ k- k. that's why you have to subtract off k- initially, you don't deposit k dollars at t= 0.

    No! k is the amount of money you deposit each month and that is a constant. At time t (months) you will have kt (k times t) not k(t) (k of t).

     
  4. Sep 25, 2007 #3
    thanks! but, another question, then....does that mean I have to start with the dif eq'n
    S' = kt + rS ?

    Cheers. =)
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: Annuity differential equation
  1. Differential equation (Replies: 4)

  2. Differential Equation (Replies: 12)

  3. Differential Equations (Replies: 1)

  4. Differential Equations (Replies: 4)

Loading...