Results 1 to 9 of 9

Math Help - investment fund question

  1. #1
    Junior Member
    Joined
    Nov 2009
    Posts
    27

    investment fund question

    A person pays $2000 into an investment fund every six months, and it earns interest at a rate of 6% pa, compounded monthly. How much is the fund worth at the end of ten years?

    Answer: $55 586.38
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Prove It's Avatar
    Joined
    Aug 2008
    Posts
    11,831
    Thanks
    1602
    Quote Originally Posted by ipokeyou View Post
    A person pays $2000 into an investment fund every six months, and it earns interest at a rate of 6% pa, compounded monthly. How much is the fund worth at the end of ten years?

    Answer: $55 586.38
    Use the formula

    A = P(1 + r)^n.

    If the rate is 6\% per year, then every month the rate is \frac{6}{12}\% = 0.5\%.

    If it is being compounded monthly for 10 years, then there are 120 time periods.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Junior Member
    Joined
    Nov 2009
    Posts
    27
    If i use the formula i would get $3638.79 which is not correct as the answer is $55 586.38

    Because i don't think that formula includes the fact that $2000 is deposited every six months for 10 years.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor
    Joined
    Dec 2007
    From
    Ottawa, Canada
    Posts
    3,170
    Thanks
    71
    Quote Originally Posted by ipokeyou View Post
    A person pays $2000 into an investment fund every six months, and it earns interest at a rate of 6% pa, compounded monthly. How much is the fund worth at the end of ten years?
    Answer: $55 586.38
    $55,586.38 is correct IF the 1st deposit is made at BEGINNING.

    The rate to be used is the semiannual rate equivalent to 6% cpd monthly,
    which is determined this way:
    (1 + r)^2 = 1.005^12 ; solve for r
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Junior Member
    Joined
    Nov 2009
    Posts
    27
    Quote Originally Posted by Wilmer View Post
    $55,586.38 is correct IF the 1st deposit is made at BEGINNING.

    The rate to be used is the semiannual rate equivalent to 6% cpd monthly,
    which is determined this way:
    (1 + r)^2 = 1.005^12 ; solve for r
    Could you show me how you got that? I don't understand where you got the LHS of the equation. And is 12 meant to be 120? I can't solve for r.
    Follow Math Help Forum on Facebook and Google+

  6. #6
    MHF Contributor
    Joined
    Dec 2007
    From
    Ottawa, Canada
    Posts
    3,170
    Thanks
    71
    (1 + r)^2 = 1.005^12 ; solve for r
    Quote Originally Posted by ipokeyou View Post
    Could you show me how you got that? I don't understand where you got the LHS of the equation. And is 12 meant to be 120? I can't solve for r.
    LHS represents a rate r compounded semiannually, hence to power 2.

    12 is meant to be 12; 12 months in a year.

    (1 + r)^2 = 1.005^12
    r = SQRT(1.005^12) - 1
    Follow Math Help Forum on Facebook and Google+

  7. #7
    Junior Member
    Joined
    Nov 2009
    Posts
    27
    Quote Originally Posted by Wilmer View Post
    (1 + r)^2 = 1.005^12 ; solve for r


    LHS represents a rate r compounded semiannually, hence to power 2.

    12 is meant to be 12; 12 months in a year.

    (1 + r)^2 = 1.005^12
    r = SQRT(1.005^12) - 1
    Oh I see. So I got r = 0.03037... and if I were to sub it into the formula A = P(1 + r)^n , with n = 120 and p = 2000 I will get 72542.82. Is this what you mean? I'm still close to the answer but not there yet. Did I use the wrong formula?
    Follow Math Help Forum on Facebook and Google+

  8. #8
    MHF Contributor
    Joined
    Dec 2007
    From
    Ottawa, Canada
    Posts
    3,170
    Thanks
    71
    Quote Originally Posted by ipokeyou View Post
    Oh I see. So I got r = 0.03037... and if I were to sub it into the formula A = P(1 + r)^n , with n = 120 and p = 2000 I will get 72542.82. Is this what you mean? I'm still close to the answer but not there yet. Did I use the wrong formula?
    That's NOT the correct formula; here:
    Future value of an annuity - Google Search=

    And n = 20, NOT 120

    r = .03037... is correct
    Follow Math Help Forum on Facebook and Google+

  9. #9
    Junior Member
    Joined
    Nov 2009
    Posts
    27
    Quote Originally Posted by Wilmer View Post
    That's NOT the correct formula; here:
    Future value of an annuity - Google Search=

    And n = 20, NOT 120

    r = .03037... is correct
    Problem solved! Thank you very much!
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. 2nd fund. theorem question on specific part
    Posted in the Calculus Forum
    Replies: 2
    Last Post: September 30th 2009, 07:16 AM
  2. Mutual Fund Question
    Posted in the Business Math Forum
    Replies: 1
    Last Post: December 2nd 2008, 07:49 AM
  3. fund question
    Posted in the Pre-Calculus Forum
    Replies: 2
    Last Post: October 7th 2008, 07:55 PM
  4. Sinking fund question
    Posted in the Business Math Forum
    Replies: 1
    Last Post: March 11th 2008, 09:55 PM
  5. Fund. Thm of Calc Question
    Posted in the Calculus Forum
    Replies: 3
    Last Post: March 1st 2008, 07:49 PM

Search Tags


/mathhelpforum @mathhelpforum