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Math Help - Algebra [newbie]

  1. #1
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    Algebra [newbie]

    I need help to understand how to work out the following formulae:

    a. (240k * Present Value Annuity(x%, 5 payments)) +
    Annual Interest
    (4M * Present Value(x%, 5 periods))
    Principal amount

    Find x

    b. 120,000 * Present Value Annuity (x%) = 309250
    Annual Lease Payment Fair Value of asset

    Find PVA (x%).
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  2. #2
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    algerbra

    Quote Originally Posted by jon80 View Post
    I need help to understand how to work out the following formulae:

    a. (240k * Present Value Annuity(x%, 5 payments)) +
    Annual Interest
    (4M * Present Value(x%, 5 periods))
    Principal amount

    Find x

    b. 120,000 * Present Value Annuity (x%) = 309250
    Annual Lease Payment Fair Value of asset

    Find PVA (x%).

    You can google for annuity equations.For specific help you need to better define problems


    bjh
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  3. #3
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    Quote Originally Posted by bjhopper View Post
    You can google for annuity equations.For specific help you need to better define problems
    bjh
    I can't figure out how to define my problem more clearly. Does it involve substitution?
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  4. #4
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    algebra

    Quote Originally Posted by jon80 View Post
    I need help to understand how to work out the following formulae:

    a. (240k * Present Value Annuity(x%, 5 payments)) +
    Annual Interest
    (4M * Present Value(x%, 5 periods))
    Principal amount

    Find x

    b. 120,000 * Present Value Annuity (x%) = 309250
    Annual Lease Payment Fair Value of asset

    Find PVA (x%).

    for each annuity state each given given value. For example A one dollar payment each month at a given annual interest rate is worth how much today after 10 year


    bjh
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  5. #5
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    Quote Originally Posted by bjhopper View Post
    for each annuity state each given given value. For example A one dollar payment each month at a given annual interest rate is worth how much today after 10 year
    bjh
    I figured out as much, but how do I carry out the substitution to find the value of x%?
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  6. #6
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    algebra

    Quote Originally Posted by jon80 View Post
    I figured out as much, but how do I carry out the substitution to find the value of x%?
    If you have PVA, PMT, N PVA/PMT = the annuity factor for Npayments at interest i.This is unusual but interest could be found easily by using a factor table which shows factors as a function on N and i.Finding i appears quite complex otherwise.

    PVA=present value of annuity
    PMT= payments to be made over n periods @ an interest of i per period.
    Annuity equations are available on line


    bjh
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  7. #7
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    Quote Originally Posted by bjhopper View Post
    If you have PVA, PMT, N PVA/PMT = the annuity factor for Npayments at interest i.This is unusual but interest could be found easily by using a factor table which shows factors as a function on N and i.Finding i appears quite complex otherwise.

    PVA=present value of annuity
    PMT= payments to be made over n periods @ an interest of i per period.
    Annuity equations are available on line


    bjh
    So how would I simplify this equation:

    309250 = 120,000 * (((1 + i) ^ 3) - 1) / i)

    Check: i should be 8%
    Links
    1. http://en.wikipedia.org/wiki/Annuity_(finance_theory)
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  8. #8
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    algebra

    [quote=jon80;473274]So how would I simplify this equation:

    309250 = 120,000 * (((1 + i) ^ 3) - 1) / i)

    Check: i should be 8%
    Links
    1. Annuity (finance theory) - Wikipedia, the free encyclopedia[/quote

    the annuity factor is 309250/120000=2.577 Using a period of 3 years the interest is indeed 8% but your annuity factor is not equal to this so your formula needs to be corrected


    bjh
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  9. #9
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    [QUOTE=bjhopper;473301]
    Quote Originally Posted by jon80 View Post
    So how would I simplify this equation:

    309250 = 120,000 * (((1 + i) ^ 3) - 1) / i)

    Check: i should be 8%
    Links
    1. Annuity (finance theory) - Wikipedia, the free encyclopedia[/quote

    the annuity factor is 309250/120000=2.577 Using a period of 3 years the interest is indeed 8% but your annuity factor is not equal to this so your formula needs to be corrected


    bjh
    hmm...interesting, however that's what wikipedia says

    So, (309250/120000 ) / 3 years = 0.86, so I'm missing something out or else the check figure is rounded up...
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  10. #10
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    Just an observation...
    3 annual payments of 120000 at 8% annually = FV of 389568
    389568 / 1.08^3 = PV of 309251.6385....

    Your equation: 309250 = 120,000 * (((1 + i) ^ 3) - 1) / i)
    Can be solved for i, but only numerically...or by iteration.
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