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Diffy Q'Shenanigans

.kbf?.kbf? Registered User regular
edited February 2010 in Help / Advice Forum
I'm having a lot of trouble with this problem and I lost my notes from the day we did interest rates :cry:

After charging $5000 to his credit card which carries a yearly interest of 20%, Bob decides to stop using his
card and to pay back $100 every month. Determine how long Bob will need to pay of his debt and how much
interest will he end up paying?

How do I set this up?

dp/dt = .2p-5000?

.kbf? on

Posts

  • 28682868 Registered User regular
    edited February 2010
    God I accidentally opened this cause I thought it may be about drinking, or my Irish roots.

    I was told there would be no math.

    2868 on
    Warhams. Allatime warhams.

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  • vonPoonBurGervonPoonBurGer Registered User regular
    edited February 2010
    I was hoping for something related to diff.

    I was also told there would be no math.

    vonPoonBurGer on
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  • PracticalProblemSolverPracticalProblemSolver Registered User regular
    edited February 2010
    PracticalProblemSolver on
  • .kbf?.kbf? Registered User regular
    edited February 2010

    I'm not just trying to plug and chug to get the interest. I need to set up and solve a differential equation.

    .kbf? on
  • PracticalProblemSolverPracticalProblemSolver Registered User regular
    edited February 2010
    okay then add differential equation to the search...

    since you seem to have the equation but can't figure it out, can't you ask your study group anyway?

    the .2p-5000 should be I * P, where I = interest rate and P = principal, so it would be .2 * 5000

    PracticalProblemSolver on
  • .kbf?.kbf? Registered User regular
    edited February 2010
    okay then add differential equation to the search...

    since you seem to have the equation but can't figure it out, can't you ask your study group anyway?

    the .2p-5000 should be I * P, where I = interest rate and P = principal, so it would be .2 * 5000

    What exactly is your problem? If you don't like me or my question you are more then welcome to not post in my thread.

    .kbf? on
  • enlightenedbumenlightenedbum Registered User regular
    edited February 2010
    Except the principal is variant, so it's not that simple, PPS.

    .kbf?:

    What does the principal change by each year?

    Also, does the question say continuously compounding interest or is it just unrealistic interest that's compounded yearly?

    enlightenedbum on
    Self-righteousness is incompatible with coalition building.
  • PracticalProblemSolverPracticalProblemSolver Registered User regular
    edited February 2010
    What? You're mad at me because I suggested two perfectly suitable avenues of research and answered your homework question instead of making jokes?

    PracticalProblemSolver on
  • 28682868 Registered User regular
    edited February 2010
    To be fair you made a joke. Let's all be friends.

    I'm in here to learn.

    I have such a phobia of math, and big debt. Christ, is this problem about me?

    As for the variant principal, and I'm bad at math here, how much of the 100 dollars is going to interest monthly? The 20 percent applies to his balance forward.

    I'm so fucking lost. But intrigued. It's like watching university challenge.

    2868 on
    Warhams. Allatime warhams.

    buy warhams
  • .kbf?.kbf? Registered User regular
    edited February 2010
    I think it's simply compounded yearly.

    So every year the new principal would be P + .2(P) - 1200? Where P is the previous total.

    .kbf? on
  • .kbf?.kbf? Registered User regular
    edited February 2010
    What? You're mad at me because I suggested two perfectly suitable avenues of research and answered your homework question instead of making jokes?

    I'm mad at you because I asked a question I can't understand and you essentially told me to fuck off. And not just once. Twice.

    .kbf? on
  • enlightenedbumenlightenedbum Registered User regular
    edited February 2010
    .kbf? wrote: »
    I think it's simply compounded yearly.

    So every year the new principal would be P + .2(P) - 1200? Where P is the previous total.

    Well, what's the change, as that's dp/dt. Also, think about when the interest is calculated. Also, double check with a TA/prof about how it's being compounded. Much easier question if it's simply yearly.

    enlightenedbum on
    Self-righteousness is incompatible with coalition building.
  • PracticalProblemSolverPracticalProblemSolver Registered User regular
    edited February 2010
    fwiw, your original formula was correct just the -5000 should have been -1200, if you do p+.2p-1200 the balance will always go up for t(0) = 5000. I was confused about what you were trying to do and probably threw you off the right track. Sorry I'm a jerk, I wasn't trying to be that much of one, enlightenedbum is nice and seems knowledgable I should just let them help you :)
    is it 8.95 years and $11989 interest? I tried it a couple different ways can't remember how to do it properly

    PracticalProblemSolver on
  • soxboxsoxbox Registered User regular
    edited February 2010
    The formula for the amount you need to pay to pay off a loan at rate r for principal P in time t is:

    L = P ( r + r / ((1+r)^t - 1))

    (That looks like a crappy form of the equation to me - my actuarial memories tell me that there should be a simpler form of that, but that was the first google).

    So, you need to rearrange that equation to solve for t.

    Note also that you'll need to change either your payment amount (L) or your interest rate depending on how often it is compounded. Is your 20% a nominal or effective interest rate?

    soxbox on
  • Fuzzy Cumulonimbus CloudFuzzy Cumulonimbus Cloud Registered User regular
    edited February 2010
    Uh, shouldn't you be doing some sort of limit or derivative?
    This is a rate of change problem.

    Fuzzy Cumulonimbus Cloud on
  • enlightenedbumenlightenedbum Registered User regular
    edited February 2010
    soxbox wrote: »
    The formula for the amount you need to pay to pay off a loan at rate r for principal P in time t is:

    L = P ( r + r / ((1+r)^t - 1))

    (That looks like a crappy form of the equation to me - my actuarial memories tell me that there should be a simpler form of that, but that was the first google).

    So, you need to rearrange that equation to solve for t.

    Note also that you'll need to change either your payment amount (L) or your interest rate depending on how often it is compounded. Is your 20% a nominal or effective interest rate?

    Again, he needs a differential equation. So he needs to think about the change in principal over time. Which he was pretty close to when last he posted but forgot something.

    enlightenedbum on
    Self-righteousness is incompatible with coalition building.
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