Results 1 to 4 of 4

Math Help - Annuities

  1. #1
    Newbie
    Joined
    Sep 2009
    Posts
    14

    Annuities

    a) Determine the present value on January 1, 2000, of payments of $200 every 6 months from January 1, 2000, through January 1, 2004, inclusive, and $100 every 6 months from July 1, 2004, through January 1, 2010, inclusive, if i = .06.

    I think it might be something like: 100(a angle 8)(0.03) + 100(a angle 20)(0.03) which equals 100((1 - v^8)/0.03) + 100((1 - v^20)/0.03) , v=1/1.03
    But the answer is $2,389.72 which is way off from what I'm getting. Am I even close?

    b) At the beginning of the year Kelly establishes a fund with a deposit of $1000. At the beginning of each month a health club withdraws a $24 fee. The fund earns a nominal rate of interest of 18% compounded monthly. Determine the amount in the fund at the end of the year.

    The only way I can think to do this is calculating each month separately so I know there's a faster way ... Any suggestions?

    Thank you!!
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Joined
    Aug 2007
    From
    USA
    Posts
    3,111
    Thanks
    2
    Quote Originally Posted by bart203 View Post
    a) Determine the present value on January 1, 2000, of payments of $200 every 6 months from January 1, 2000, through January 1, 2004, inclusive, and $100 every 6 months from July 1, 2004, through January 1, 2010, inclusive, if i = .06.

    I think it might be something like: 100(a angle 8)(0.03) + 100(a angle 20)(0.03) which equals 100((1 - v^8)/0.03) + 100((1 - v^20)/0.03) , v=1/1.03
    But the answer is $2,389.72 which is way off from what I'm getting. Am I even close?

    b) At the beginning of the year Kelly establishes a fund with a deposit of $1000. At the beginning of each month a health club withdraws a $24 fee. The fund earns a nominal rate of interest of 18% compounded monthly. Determine the amount in the fund at the end of the year.

    The only way I can think to do this is calculating each month separately so I know there's a faster way ... Any suggestions?

    Thank you!!
    a) The first piece has 9 of those $200 payments. It's an annuity due.
    a) Make up your mind on the number of $100 payments. It looks like 12 to me.
    b) You must learn to use "Basic Principles".

    if r = 1 + 0.18/12 = 1.015

    At the end of the year, we have

    1000r^12 -24(r^12 + r^11 + ... + r^1)

    You should be able to add the 12 values in the parentheses and you will nearly be done.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Banned
    Joined
    Dec 2007
    From
    Ottawa, Canada
    Posts
    3,184
    Thanks
    80
    Quote Originally Posted by bart203 View Post
    b) At the beginning of the year Kelly establishes a fund with a deposit of $1000. At the beginning of each month a health club withdraws a $24 fee. The fund earns a nominal rate of interest of 18% compounded monthly. Determine the amount in the fund at the end of the year.
    Simply pretend this is a $1000 loan at monthly payments of $24,
    rate .18/12 per month; what is loan balance after 12 payments?
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Banned
    Joined
    Dec 2007
    From
    Ottawa, Canada
    Posts
    3,184
    Thanks
    80
    Quote Originally Posted by bart203 View Post
    a) Determine the present value on January 1, 2000, of payments of $200 every 6 months from January 1, 2000, through January 1, 2004, inclusive, and $100 every 6 months from July 1, 2004, through January 1, 2010, inclusive, if i = .06.
    Interest rate is WHAT? i = .06 means every 6 months, from .12/2 = .06;
    get that straightened out.

    With these, sometimes easier to "see" using future value:
    1) future value of payments of $200 to Jan.1/04
    2) future value of above to Jan.1/10
    3) future value of payments of $100 for same period as in 2)
    Add 'em up, calculate present value.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Help with annuities due.
    Posted in the Business Math Forum
    Replies: 3
    Last Post: December 7th 2011, 11:03 AM
  2. [SOLVED] Ordinary Annuities and Annuities help
    Posted in the Business Math Forum
    Replies: 6
    Last Post: December 5th 2011, 02:04 PM
  3. Annuities
    Posted in the Business Math Forum
    Replies: 0
    Last Post: September 22nd 2010, 12:24 AM
  4. Help with annuities!
    Posted in the Business Math Forum
    Replies: 7
    Last Post: May 30th 2010, 10:10 PM
  5. Deferred Annuities
    Posted in the Business Math Forum
    Replies: 0
    Last Post: March 15th 2007, 12:23 PM

Search Tags


/mathhelpforum @mathhelpforum