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Math Help - [SOLVED] Help with annuity question

  1. #1
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    Jan 2009
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    Exclamation [SOLVED] Help with annuity question

    Here is what is given:

    PV = $5,000
    PMT = $200
    i = .01
    n=?

    5000=200(1-(1.01)-n)
    .01
    I know that this is lining exactly up right but it shows the general idea of the problem.

    The problem, and I can't figure out where this comes from, is that the book shows the next step as:

    =20,000[1-(1.01)-n] and I don't know where the 20,000 came from. Is there a step that I missed. I'm trying to solve for "n" in this problem and everything that I try comes up with approximately 22 periods but the answer should be 29.
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  2. #2
    Member
    Joined
    Apr 2008
    Posts
    83
    Quote Originally Posted by lynnmpward View Post
    Here is what is given:

    PV = $5,000
    PMT = $200
    i = .01
    n=?

    5000=200(1-(1.01)-n)
    .01

    I know that this is lining exactly up right but it shows the general idea of the problem.

    The problem, and I can't figure out where this comes from, is that the book shows the next step as:

    =20,000[1-(1.01)-n] and I don't know where the 20,000 came from. Is there a step that I missed. I'm trying to solve for "n" in this problem and everything that I try comes up with approximately 22 periods but the answer should be 29.
    Should be
    5,000=200*(1-(1.01)^n)/0.01
    Looks better this way
    <br />
5,000 = 200 \cdot \frac{{1 - \left( {1.01} \right)^{ - n} }}{{0.01}} \Leftrightarrow 5,000 = 200 \cdot \frac{{1 - {\textstyle{1 \over {\left( {1.01} \right)^n }}}}}{{0.01}}<br />
    Now solve for n if you're already familiar with logarithms. Are you?
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