Results 1 to 2 of 2

Math Help - superannuation

  1. #1
    Junior Member
    Joined
    Nov 2009
    Posts
    45

    superannuation

    An amount of $1500 is invested at a rate of 4.5% per annum with the interest compounded monthly. How long will it take for the investment to double its value?


    Im unclear as to why they use this formula : 1500 (1+4.5/1200)^t = 3000
    If someone could explain this to me, it would be greatly appreciated, thank you
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    Aug 2008
    From
    Paris, France
    Posts
    1,174
    Quote Originally Posted by christina View Post
    An amount of $1500 is invested at a rate of 4.5% per annum with the interest compounded monthly. How long will it take for the investment to double its value?


    Im unclear as to why they use this formula : 1500 (1+4.5/1200)^t = 3000
    If someone could explain this to me, it would be greatly appreciated, thank you
    When a bank says that the interest rate is 4.5% with interest compounded monthly, that means that after each month your investiment I grows by \frac{4.5\%}{12} (=4.5/1200 or 0.045/12), so that it becomes I_1 = I+\frac{0.045}{12}I=I\left(1+\frac{0.045}{12}\righ  t). After another month, the interest is computed from what you now have (i.e. I_1), thus after two months you have I_2=I_1+\frac{0.045}{12}I_1=I\left(1+\frac{0.045}{  12}\right)^2 and so on, after n month you have I_n=I \left(1+\frac{0.045}{12}\right)^n.

    Note that after one year you have \left(1+\frac{0.045}{12}\right)^{12}\simeq 1.0459, thus the annual rate is a bit more than 4.5%. If I were a bankier, I would define the monthly rate to be \left(1+0.045\right)^{1/12}-1, it would make more sense! (especially if I am the bankier)
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Superannuation
    Posted in the Business Math Forum
    Replies: 4
    Last Post: December 4th 2011, 06:14 AM
  2. superannuation/pensions
    Posted in the Business Math Forum
    Replies: 2
    Last Post: March 20th 2010, 03:36 PM
  3. Superannuation
    Posted in the Business Math Forum
    Replies: 1
    Last Post: February 4th 2010, 07:42 PM
  4. Tricky Superannuation Problem
    Posted in the Business Math Forum
    Replies: 5
    Last Post: August 14th 2009, 02:24 PM
  5. Superannuation
    Posted in the Business Math Forum
    Replies: 2
    Last Post: July 8th 2009, 04:07 PM

Search Tags


/mathhelpforum @mathhelpforum