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Math Help - Finite Math: Annuities!

  1. #1
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    Finite Math: Annuities!

    Im having problems trying to figure out how to solve this problem.

    The formula for Future Value of an Ordinary Annuity is

    FV=PMT( (1+I)^n -1)/I)

    The problem isFind the I (rate per period) and the N( number of Periods) for each annuity.

    Quarterly deposits of $500 are made for 20 years into an annuity that pays 8% coumpounded quarterly.

    fv=500((1+.08/4)^20-1)/.08

    Since it is deposited quarterly do i multiply 500x4? and since it is compounded quarterly do I divide both interest by 4?

    help! thanks
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  2. #2
    Member jonah's Avatar
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    Quote Originally Posted by lunaj View Post
    fv=500((1+.08/4)^20-1)/.08
    should be
    fv=500((1+.08/4)^(20*4)-1)/(.08/4)
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  3. #3
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    Thanks!

    When a question says that a certain amount is deposited x number of times a year, do i ignore that and just divide the interest and multiply n by the # compunded??

    In this case $500 is deposited quarterly and the whole thing is coumpounded quarterly, so it all works out to 4.

    what if $500 is deposited every month and coumpounded quarterly?
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  4. #4
    Member jonah's Avatar
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    Quote Originally Posted by lunaj View Post
    When a question says that a certain amount is deposited x number of times a year, do i ignore that and just divide the interest and multiply n by the # compunded??
    Kinda
    Quote Originally Posted by lunaj View Post
    In this case $500 is deposited quarterly and the whole thing is coumpounded quarterly, so it all works out to 4.

    what if $500 is deposited every month and coumpounded quarterly?
    Then you have a complex or general annuity problem.
    You need to convert the quarterly rate into its equivalent monthly rate.
    One way of doing this is to equate the effective rate of say 8% compounded quarterly as given by
    <br />
w_{{\text{compounded quarterly}}}  = \left( {1 + \frac{{.08}}<br />
{4}} \right)^4  - 1<br />
    with the effective rate of j% compounded monthly which is given by
    <br />
w_{{\text{compounded monthly}}}  = \left( {1 + \frac{j}<br />
{{12}}} \right)^{12}  - 1<br />
    You then solve for j.
    After that, you merely replace 8% with j and 4 with 12 in your corrected formula.
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  5. #5
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    Do do both of these for one problem?

    ex

    500( 1+.08/12)^12-1/.08/12 and then i multiply this answer the same way but compunded quarterly?

    im confused
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  6. #6
    Member jonah's Avatar
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    Quote Originally Posted by lunaj View Post
    Do do both of these for one problem?

    ex

    500( 1+.08/12)^12-1/.08/12 and then i multiply this answer the same way but compunded quarterly?

    im confused
    should be
    500[( 1+j/12)^(20*12)-1]/(j/12)
    but you must first equate the right hand side of

    with the right hand side of

    and solve for j.
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