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How do you show the number of subsets of a set is 2^n?

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  • #46
    Hello, can anyone help me with this compound interest formula?

    I was reading this article:

    "Compound interest means that interest is added to the principal after each period, and therefore accrues additional interest. Interest payments on savings accounts and some CDs is compounded at a regular rate. Transforming an annual interest rate into a compounded daily periodic rate is done through the equation at left, where r1 is the annual interest rate, n1 is equal to one, r2 is the daily periodic rate and n2 is the number of compounding periods in a year (either 360 or 365). If interest is compounded daily, the 2 percent annual rate quoted in the previous example increases to 0.005534246 percent on a daily periodic basis of 365."



    I'm trying to determine how the author arrived at a figure of 0.005534246% interest compounded daily on a 2% annual interest rate.

    When I run the figures through the formula I get 0.019803164% daily periodic interest.

    What am I missing?

    Original article:

    http://www.ehow.com/how-does_4927638...alculated.html

    Comment


    • #47
      Originally posted by Zeigy View Post
      Hello, can anyone help me with this compound interest formula?

      I was reading this article:

      "Compound interest means that interest is added to the principal after each period, and therefore accrues additional interest. Interest payments on savings accounts and some CDs is compounded at a regular rate. Transforming an annual interest rate into a compounded daily periodic rate is done through the equation at left, where r1 is the annual interest rate, n1 is equal to one, r2 is the daily periodic rate and n2 is the number of compounding periods in a year (either 360 or 365). If interest is compounded daily, the 2 percent annual rate quoted in the previous example increases to 0.005534246 percent on a daily periodic basis of 365."



      I'm trying to determine how the author arrived at a figure of 0.005534246% interest compounded daily on a 2% annual interest rate.

      When I run the figures through the formula I get 0.019803164% daily periodic interest.

      What am I missing?

      Original article:

      http://www.ehow.com/how-does_4927638...alculated.html
      (1 + .02)^(1/365) - 1

      How did you come up with 0.019803164%? Did you mean you came up with 0.019803164? which is 1.9803164% (and did you do that by multiplying the above by 365).

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      • #48
        I came up with 0.019803164. You're right the figures I quoted form the article are correct but my resultant answer I incorrectly quoted as 0.019803164%. I meant 1.9803164% was the answer I got after multiplying by 365.

        I'm trying to figure out why my figure of 1.9803164% doesn't match up with the articles figure of 0.005534246%. Aren't both these figures interest compounded daily on an annual rate of 2%? Obviously not but what am I doing wrong?

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        • #49
          The formula is

          (1+i) = (1 + i^(n) / n)^n

          So if we solve for i^(n) / n we get

          (1+i)^(1/n) - 1 = i^(n) / n

          You solved for i^(n)
          Last edited by NoMoreExams; January 28 2012, 01:52 AM.

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          • #50
            Thank you for the reply. I'm going to have a look at it.

            Comment


            • #51
              Originally posted by NoMoreExams View Post
              1) What about points of inflection? What about on a closed interval, etc.

              2) I meant what's the definition of maximum not maximum of a function i.e. define for me max{X,Y}
              For a function:
              Let f be a function that is defined and continuous on the closed interval [a,b].

              Suppose x is a point within the interval [a,b] and that a < x < b.

              A maximum is said to exist at point x when f(x) > f(c) for all c in [a,b]. A minimum is said to occur at point x when f(x) < f(c) for all c within [a,b].

              For a set:
              Let S be a set.

              max(S) is the element c in S, such that c > or = a for all a in S.

              Annnnnnnd I just realized how old your post is. Sorry, I'm posting anyways. Took some thinking on my part and I'm not letting it go to waste.

              Comment


              • #52
                Originally posted by bsd058 View Post
                For a function:
                Let f be a function that is defined and continuous on the closed interval [a,b].

                Suppose x is a point within the interval [a,b] and that a < x < b.

                A maximum is said to exist at point x when f(x) > f(c) for all c in [a,b]. A minimum is said to occur at point x when f(x) < f(c) for all c within [a,b].

                For a set:
                Let S be a set.

                max(S) is the element c in S, such that c > or = a for all a in S.

                Annnnnnnd I just realized how old your post is. Sorry, I'm posting anyways. Took some thinking on my part and I'm not letting it go to waste.
                All I wanted him to say is max{X,Y} = X if X > Y and Y otherwise

                Comment


                • #53
                  Originally posted by NoMoreExams View Post
                  All I wanted him to say is max{X,Y} = X if X > Y and Y otherwise
                  Oh I see. Defining specifically max{X, Y}, and not just max of S any set. Sounded like he was all over the place. Maybe I'll understand more when I study for FM.

                  Comment

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