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Math Help - Help!!!

  1. #1
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    Joined
    Feb 2007
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    5

    Help!!!

    Henry intends to retire in 14 years and would like to receive $2472 every six months for 19 years starting on the date of his retirement. How much must Henry deposit in an account today if interest is 6.65% compounded semi-annually?
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  2. #2
    Super Member

    Joined
    May 2006
    From
    Lexington, MA (USA)
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    Hello, Julie!

    You need a couple of important formulas for this problem.
    If you don't know them, I don't see how you can expect to solve it.


    Henry intends to retire in 14 years and would like to receive $2472
    every six months for 19 years starting on the date of his retirement.
    How much must Henry deposit in an account today
    if interest is 6.65% compounded semi-annually?

    Upon his retirement, he must have A dollars investing in a "sinking fund".
    It will earn 6.65% interest compounded semi-annually and allow him to
    withdraw $2472 every six months for 19 years before the funds are depleted.

    . . . . . . . . . . . . . . . . . . .(1 + i)^n - 1
    The formula is: . A . = . D----------------
    . . . . . . . . . . . . . . . . . . . i(1 + i)^n

    . . where: A = amount invested, D = periodic withdrawl,
    i = periodic interest rate, n = number of periods.

    . . . . . . . . . . . . . . . . . . . (1.03325)^{38} - 1
    We have: . A . = . 2472------------------------------- . . $54,374.53
    . . . . . . . . . . . . . . . . . (0.03325)(1.03325)^{38}

    He must have this amount to invest upon his retirement.
    Hence, he must deposit a certain amount (P) now.


    The compound interest formula is: . A .= .P(1 + i)^n . . P .= .A/(1 + i)^n

    We have: .i = 0.03325, n = 28, A = 54,374.53

    . . Hence: . P . = . 54,374.53/(1.03325)^{28} . . $21,759.25

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  3. #3
    Newbie
    Joined
    Feb 2007
    Posts
    5

    Thanks

    I used a different formula and my answer was different by 1,479.84.
    this is the formula i used:
    PV= PMT[ 1- (1+i)^-n]/i
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