Results 1 to 7 of 7
Like Tree1Thanks
  • 1 Post By DenisB

Thread: L'il annuity escapade!

  1. #1
    MHF Contributor
    Joined
    Feb 2015
    From
    Ottawa Ontario
    Posts
    1,671
    Thanks
    313

    L'il annuity escapade!

    Devised by yours truly, for your enjoyment!

    12 annual payments of same amount are deposited (at year-end)
    in an account, resulting in $30,000 at end of 12th year.
    4 different annual interest rates are used, as following:
    years 1 to 3: 6%
    years 4 to 6: 8%
    years 7 to 9: 10%
    years 10 to 12: 12%

    Calculate the payment amount.
    Thanks from topsquark
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    Apr 2005
    Posts
    19,337
    Thanks
    2859

    Re: L'il annuity escapade!

    Starting with amount A, first month earned .06A interest so at the end of the first month A+ 0.06A= (1.06)A in the account. Second month earned 0.6(1.06)A interest so at the end of the second month, (1.06)A+ .06(1.06)A= (1.06A)(1+ .06)= A(1.06)^2 in the account. Get the idea? For the first 3 years, the amount in the account after n months was A(1.06)^n. There are 36 months in 3 years so at the end of the third year there was A(1.06)^36= 8.1472519998510757482226489017467A which I would be incline to round off to 8.14725A.

    Now do the same thing for the next 36 months, using 8.14725A in place of A and 1.08 in place of 1.06, etc. Once you have calculated the amount after all 12 years, as a number times A, set it equal to $30,000 and solve for A.
    Last edited by HallsofIvy; Jul 13th 2016 at 10:35 AM.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor
    Joined
    Feb 2015
    From
    Ottawa Ontario
    Posts
    1,671
    Thanks
    313

    Re: L'il annuity escapade!

    Try again: no months involved (I wouldn't be that cruel!).
    Annual payments, rates given = annual rates...
    Balance end year 1: A
    Balance end of year 2: A + 1.06A
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Senior Member
    Joined
    Jun 2014
    From
    Illinois
    Posts
    263
    Thanks
    91

    Re: L'il annuity escapade!

    I get $1389.23 as the annual payment.
    Follow Math Help Forum on Facebook and Google+

  5. #5
    MHF Contributor
    Joined
    Feb 2015
    From
    Ottawa Ontario
    Posts
    1,671
    Thanks
    313

    Re: L'il annuity escapade!

    Right on, Chipper!
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Member jonah's Avatar
    Joined
    Apr 2008
    Posts
    226
    Thanks
    27

    Re: L'il annuity escapade!

    Beer soaked ramblings follow.
    To indulge my old friend Sir Denis and for Sir Hallsofivy's enlightenment:

    What is R in

    R*[(1.12)^3-1]/.12+R*[(1.10)^3-1]/.10*(1.12)^3+R*[(1.08)^3-1]/.08*(1.10)^3*(1.12)^3+R*[(1.06)^3-1]/.06*(1.08)^3*(1.10)^3*(1.12)^3=30,000
    Follow Math Help Forum on Facebook and Google+

  7. #7
    MHF Contributor
    Joined
    Feb 2015
    From
    Ottawa Ontario
    Posts
    1,671
    Thanks
    313

    Re: L'il annuity escapade!

    NICE Sir Jonah. My approach:

    R1 = .06 : a = (1 + R1)^3
    R2 = .08 : b = (1 + R2)^3
    R3 = .10 : c = (1 + R3)^3
    R4 = .12 : d = (1 + R4)^3

    u = (a - 1)*b*c*d / R1
    v = (b - 1)*c*d / R2
    w = (c - 1)*d / R3
    x = (d - 1) / R4

    P = annual payment

    P = 30000 / (u + v + w + x)

    HINT: P = ?,???.2318793...
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Li'l right triangle escapade...
    Posted in the Math Puzzles Forum
    Replies: 6
    Last Post: Jul 5th 2016, 04:52 PM
  2. Financial escapade
    Posted in the Business Math Forum
    Replies: 7
    Last Post: Jul 13th 2015, 08:11 AM
  3. Annuity
    Posted in the Business Math Forum
    Replies: 12
    Last Post: Jul 11th 2010, 09:06 AM
  4. Annuity Due
    Posted in the Business Math Forum
    Replies: 4
    Last Post: Nov 8th 2009, 02:20 PM
  5. another annuity
    Posted in the Math Topics Forum
    Replies: 1
    Last Post: Sep 27th 2008, 07:15 PM

Search Tags


/mathhelpforum @mathhelpforum