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Math Help - [SOLVED] Annuities

  1. #1
    Ife
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    [SOLVED] Annuities

    I am not sure what's the correct approach to this question. Can I get some guidance please??

    As part of a retirement package for a local oil company, Jerry will receive $36,000 every 6 months for the next 20 years.
    If the funds to fund this pension are invested at a rate of J_1 = 8 \%, how much money is there initially in the fund?

    I am getting an equivalent interest rate: J_2 = 0.0392, and a present value for the total payments to be 991,741. Whats the correct thing to do??
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  2. #2
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    Quote Originally Posted by Ife View Post
    I am not sure what's the correct approach to this question. Can I get some guidance please??

    As part of a retirement package for a local oil company, Jerry will receive $36,000 every 6 months for the next 20 years.
    If the funds to fund this pension are invested at a rate of J_1 = 8 \%, how much money is there initially in the fund?

    I am getting an equivalent interest rate: J_2 = 0.0392, and a present value for the total payments to be 991,741. Whats the correct thing to do??
    .0392 is correct (3.92304845...%) IF 8% is effective annually;
    if rate is 8% annual compounded semiannually, then use .04

    991,741 is way too high; should be ~720,773
    Try again.
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  3. #3
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    Okay, I am not sure if I am totally correct but here's how i did it.

    use the present value formula, PV=R[(1-(1+i)^-n)/i]

    since Jerry receives $ 36,000 every 6 months

    then R(regular payment)=36,000,
    n(compounding periods)= 20x2=40(12/6=2) , and
    i(interest rate per compounding period)= 8%(.08/2)=0.04

    sub. all the values into the formula and solve for PV and it will be the value of the initial fund.

    turn out to be approximately $712,539.86 which is the same as what Wilmer suggested.

    Hope this helps. =]
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  4. #4
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    That's correct, Fury, IF rate is 4% per 6months;
    this then results in annual rate of 1.04^2 - 1 = .0816, or 8.16%.

    IF annual rate is to be 8% (not 8.16) then 3.92% per 6months MUST be used.
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