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Math Help - Another annuity problem?

  1. #1
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    Another annuity problem?

    I haven't seen nor been able to calculate this particular annuity, here's the narrative.

    If I deposit $1000 every other week (26 payments per year), with a constant interest rate of 8%, which is paid at the end of the month and rolled into the annuity, how much interest will occur per month? What will the n year value of the annuity be? For example, how about after year 8?

    - Matt
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  2. #2
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    Something wrong with that "narrative"...IF formula to be used.
    Assume January's are on Jan 14 and Jan 28 ; so interest 3 days later?
    To use financial formulas, stuff must coincide.

    Only way I can see handling your problem is by a special program
    to fit it, feeding dates and the likes...
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  3. #3
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    Quote Originally Posted by mgargett View Post
    I haven't seen nor been able to calculate this particular annuity, here's the narrative.

    If I deposit $1000 every other week (26 payments per year), with a constant interest rate of 8%, which is paid at the end of the month and rolled into the annuity, how much interest will occur per month? What will the n year value of the annuity be? For example, how about after year 8?

    - Matt
    A rational approximation can be achieved.

    i = 0.08

    i^{(12)} = 0.08/12

    i^{(26)} = \left[(1+i^{(12)})^{6/13}\right]-1

    This does assume that all months are the same size and that years of 364 days. That's close enough for many things.
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  4. #4
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    approx's

    Different ways to get approximations; here's 3 (1st year results):

    1: assume 1000*26 / 12 = 2166.67 is the monthly deposit (.08/12) : 26,975

    2: assume monthly deposit of 2000, plus 1000 Mar 31 and Sep 30 (.08/12) : 26,982

    3: assume 26 deposits of 1000 (26 cpd periods @ .08/26) : 27,025

    In each case, interest rate used can be adjusted (lowered) in a manner
    to represent 8% effective.

    Do you agree, Mr Hunny?
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  5. #5
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    There are, indeed, infinitely many ways to approximate the result. There is only one way that your financial institution actually calculates the result.

    If you REALLY want the monthly interest, for different sized months, no approximation will be sufficient. In fact, I will stick my neck out here and state rather flatly that the approximations are more reasonable over longer periods. A month is very short. A year is better.
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  6. #6
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    get sample statement?

    Using this case as example, you could ask your Banker:
    ok, if I deposit $1000 every 2 weeks this year, 1st one being Jan 2nd,
    and you pay me this mysterious 8% on last day of each month,
    how much exactly will be in my account on Dec 31st ?

    When he tells you the amount, then you can floor him by mentally
    subtracting $26,000 from that amount, and announcing: so you'll
    give $X in interest!
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