Results 1 to 8 of 8

Math Help - future value of an ordinary simple annuity

  1. #1
    Member
    Joined
    Nov 2008
    From
    windsor ont cAN
    Posts
    87

    future value of an ordinary simple annuity

    You can purchase a residential building lot for $60 000 cash or for $10 000 down and month-end payments of $1000 for five years. If money is worth 7.5% compounded monthly, which option should you chose?

    i was part way to the answer when i encounterd a problem.

    Using the formula FV= P ( 1 + r/n ) ^ n * t [for option 1]

    where P = 60 000
    t = 5
    n = 12 60 000 ( 1 + 0.075/12 ) ^ 12 * 5

    323 289.7797

    for option 2 however ,

    i'm confused on the same formula as suppose to a different one.
    Different meaning FV = PMT [ 1 - ( 1 + i )^-n / i ]

    i want to be abe to arrive at correct answer using
    FV= P ( 1 + r/n ) ^ n * t
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Joined
    Dec 2007
    From
    Ottawa, Canada
    Posts
    3,102
    Thanks
    68
    Quote Originally Posted by diehardmath4 View Post
    Using the formula FV= P ( 1 + r/n ) ^ n * t [for option 1]
    where P = 60 000
    t = 5
    n = 12
    60 000 ( 1 + 0.075/12 ) ^ 12 * 5
    323 289.7797
    Don't you think that's a bit high; if I lend you $60,000 will you
    pay me back over $323,000?

    Should be:
    60 000 ( 1 + 0.075/12 ) ^ (12 * 5)
    = 60 000 ( 1 + 0.075/12 ) ^ 60 = ~87,198
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Member
    Joined
    Nov 2008
    From
    windsor ont cAN
    Posts
    87
    i must have forgotten to bracket the exponent ( 12 * 5 ) thanks for pointing that out. But still the 2nd option is unclear
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Member
    Joined
    Nov 2008
    From
    windsor ont cAN
    Posts
    87
    Actually This question isn't about lending money . It's about owning a condo and out of the two options which one is the better one.
    Follow Math Help Forum on Facebook and Google+

  5. #5
    MHF Contributor
    Joined
    Dec 2007
    From
    Ottawa, Canada
    Posts
    3,102
    Thanks
    68
    Quote Originally Posted by diehardmath4 View Post
    for option 2 however ,
    i'm confused on the same formula as suppose to a different one.
    Different meaning FV = PMT [ 1 - ( 1 + i )^-n / i ]
    i want to be abe to arrive at correct answer using
    FV= P ( 1 + r/n ) ^ n * t
    Many things we "WANT" are impossible!!

    This formula: FV = PMT [{ 1 - ( 1 + i )^-n }/ i ] (notice extra brackets!)
    MUST be used when dealing with payments (like your $1000 per month).

    This formula: FV= PV ( 1 + i) ^ n
    is used ONLY if there are no payments, but a Present Value (like your $60000).

    i = .075/12, n = 60

    Option 1:
    60000(1 + i)^n = ~87,198

    Option 2:
    10000(1 + i)^n = ~14,533 (the 10,000 is treated same as the 60,000)
    1000[{ 1 - ( 1 + i )^-n} / i ] = ~72,527
    Add 'em up: ~87,060

    Pretty close, hey?

    By the way, were you TOLD to use Future Values?
    Much faster/easier to use Present Values.
    Follow Math Help Forum on Facebook and Google+

  6. #6
    MHF Contributor
    Joined
    Dec 2007
    From
    Ottawa, Canada
    Posts
    3,102
    Thanks
    68
    Something else...but this is kind of "my way", so just a suggestion:

    Take the PMT equation:
    FV = PMT [{ 1 - ( 1 + i )^-n }/ i ]

    Kinda confusing-looking, right?

    FV = PMT(x / i) where x = 1 - ( 1 + i )^-n

    Much easier to "see", right?
    Follow Math Help Forum on Facebook and Google+

  7. #7
    Member
    Joined
    Nov 2008
    From
    windsor ont cAN
    Posts
    87
    Option 2:
    10000(1 + i)^n = ~14,533 (the 10,000 is treated same as the 60,000)
    1000[{ 1 - ( 1 + i )^-n} / i ] = ~72,527
    Add 'em up: ~87,060

    10 000 ( 1 + 0.075/12)^12 = 10 776.33 ( mistake? )

    1000 [ 1 - ( 1 + 0.075/12)^-60 / 0.075 ] = 90 745.58 ( mistake? )
    Follow Math Help Forum on Facebook and Google+

  8. #8
    MHF Contributor
    Joined
    Dec 2007
    From
    Ottawa, Canada
    Posts
    3,102
    Thanks
    68
    Quote Originally Posted by diehardmath4 View Post
    Option 2:
    10000(1 + i)^n = ~14,533 (the 10,000 is treated same as the 60,000)
    1000[{ 1 - ( 1 + i )^-n} / i ] = ~72,527
    Add 'em up: ~87,060

    > 10 000 ( 1 + 0.075/12)^12 = 10 776.33 ( mistake? )

    No. 10 000 ( 1 + 0.075/12)^60

    > 1000 [ 1 - ( 1 + 0.075/12)^-60 / 0.075 ] = 90 745.58 ( mistake? )

    Sorry; typed PV formula (but used FV; 72,527 is correct):
    FV = 1000[(1 + i)^n - 1)] / i
    = 1000[(1 + .075/12)^60 - 1)] / (.075/12) = ~72,527
    .
    Last edited by Wilmer; August 10th 2009 at 01:27 PM. Reason: none
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. formula for future value of immediate annuity
    Posted in the Business Math Forum
    Replies: 6
    Last Post: September 24th 2011, 06:10 AM
  2. Present value of an ordinary simple annuity
    Posted in the Business Math Forum
    Replies: 1
    Last Post: April 9th 2010, 05:23 AM
  3. Present Value of an ordinary simple annuity
    Posted in the Business Math Forum
    Replies: 3
    Last Post: April 1st 2010, 06:23 PM
  4. present value of an ordinary simple annuity
    Posted in the Business Math Forum
    Replies: 1
    Last Post: March 29th 2010, 07:35 PM
  5. Future Value of an Annuity Problem-HELP!!
    Posted in the Business Math Forum
    Replies: 1
    Last Post: September 25th 2008, 08:43 AM

Search Tags


/mathhelpforum @mathhelpforum