Results 1 to 4 of 4

Math Help - Finding the Differential

  1. #1
    Newbie
    Joined
    Jul 2009
    Posts
    3

    Finding the Differential

    Ian contributes $2000 a month into an account earning interest at a rate of r/year compounded monthly. At the end of 25 years his account will be worth

    S=((24000[(1+(r/12))^(300)-1])/(r))


    Find the differential of S.

    I'm having trouble calculating the derivative of this equation because there are so many mixed operations. I know the differential is S^(prime)(r)(dy/dx)x but how can I find the differential if I can't find the derivative?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Joined
    Mar 2007
    Posts
    1,240

    Question

    Is the following the general formula for payment amount P, at annual interest rate r, with the interest compounded m times a year over t years, with i\, =\, \frac{r}{m} and n\, =\, tm?

    . . . . . S\, =\, P\left[\frac{(1\, +\, i)^n\, -\, 1}{i}\right]

    If so, are you trying to find dS in terms of r and dr?
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Jul 2009
    Posts
    3
    Yes, that's what I'm trying to do. I need to find out the change in S when r increases from 9% to some another percentage.

    The question asks me to find how much more would Ian's account be worth if he earned 9.1% instead of 9%, and so on. I know that I can simply plug in .009 and .0091 into the equation and do S(.009)-S(.0091) but the question is asking me to estimate?
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Newbie
    Joined
    Jul 2009
    Posts
    3
    <br /> <br />
S\, =\, 24000\left[\frac{(1\, +\, i)^{300}\, -\, 1}{i}\right]<br />

    This is the equation the book gives me for the value of his account after 25 years and it wants me to find the derivative of it. When I plug it into my ti89 calculator my denominator gets astronomically large.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Finding a differential.
    Posted in the Calculus Forum
    Replies: 3
    Last Post: July 13th 2011, 12:10 PM
  2. Finding the differential of dy
    Posted in the Calculus Forum
    Replies: 5
    Last Post: July 20th 2010, 11:55 PM
  3. finding a differential eq.
    Posted in the Differential Equations Forum
    Replies: 0
    Last Post: March 7th 2010, 01:21 AM
  4. finding differential
    Posted in the Calculus Forum
    Replies: 3
    Last Post: November 7th 2009, 02:24 PM
  5. Finding this differential
    Posted in the Calculus Forum
    Replies: 1
    Last Post: November 22nd 2008, 09:19 AM

Search Tags


/mathhelpforum @mathhelpforum