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Math Help - Help with annuities due.

  1. #1
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    Help with annuities due.

    Also ya know show me the formulas for annuities due?

    The instructions in the book are: Find the amount of the following annuities due if interest is compounded annually. Find the amount of interest earned.

    R= $1200 i=o.075 n=8
    Answer in back of book
    $13,475.82
    $3875,82

    R=$17544 i=0.08 n=10
    Answer in back of book
    $138,997.66
    $33,733.66
    Last edited by mr fantastic; December 6th 2011 at 11:47 AM. Reason: Title.
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  2. #2
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    Re: Help with annuities due.

    i would hope these formulae are in your textbook.

    Notation varies by country and teacher, the formulae i was taught are:

    Definitions
    i = interest rate (compounded once per period)
    n = number of periods
    S = total payment per period
    FV = future value
    d = rate of discount

    formulae
    d = \frac{i}{1+i}
    FV = S \frac{(1+i)^n - 1}{d}

    Answer
    subbing your numbers in (i assume R was the annual payment):
    d = 0.075/1.075 = 0.069767
    FV = 1200 \times \frac{1.075^8 - 1}{0.069767} = 13475.82

    Now, for the interest earned. The final value must be equal to the Cash invested plus interest., so

    13475.82 = (cash invested) + (interest paid)

    You know that the cash invested is 1200*8, so:

    13475.82 = 1200 \times 8 + (interest~paid)
    3875.82 = (interest~paid)

    You try the other one.

    A more detailed overview of annuity formulae is here if required:
    http://www.mathhelpforum.com/math-he...gfan+annuities
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  3. #3
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    Re: Help with annuities due.

    So what's the formula for interest earned? I forget which is the interest paid and how to do so and I couldn't find it in that link you provided.
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  4. #4
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    Re: Help with annuities due.

    Quote Originally Posted by SpringFan25 View Post
    Now, for the interest earned. The final value must be equal to the Cash invested plus interest., so

    13475.82 = (cash invested) + (interest paid)

    You know that the cash invested is 1200*8, so:

    13475.82 = 1200 \times 8 + (interest~paid)
    3875.82 = (interest~paid)
    as above
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