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Thread: Equivilent Cash Price

  1. #1
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    Equivilent Cash Price

    Hi guys,

    I was wondering if someone could confirm or assist in this problem with the current answer I have?

    Problem:

    A student bought a rental property for $60 000.00 down and monthly payments of $1500.00 for 5 years. What is the equivalent cash price if money is worth 5.75% compounded semi-annually?

    Answer:

    PMT = 1500; I = 5.75%/2 = 0.02875; n = 5(12) = 60;
    PV = 1500[1 – (1.02875)-60 / 0.02875](1.02875)
    = 1500(28.434645)(1.02875)
    = 42651.97(1.02875)
    = $43878.21
    The equivalent cash price is $43,878.21

    Thanks very much
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  2. #2
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    Re: Equivilent Cash Price

    Quote Originally Posted by Sharks12 View Post
    A student bought a rental property for 60 000.00 down and monthly
    payments of 1500.00 for 5 years. What is the equivalent cash price
    if money is worth 5.75% compounded semi-annually?

    Answer:

    PMT = 1500; I = 5.75%/2 = 0.02875; n = 5(12) = 60;
    PV = 1500[1 – (1.02875)-60 / 0.02875](1.02875)
    = 1500(28.434645)(1.02875)
    = 42651.97(1.02875)
    = $43878.21
    Sorry...but that's way off...

    First, semi-annual rate must be converted to annual equivalent:
    s = (1 + .0575/2)^2

    Then I is calculated as the monthly rate to achieve above:
    I = s^(1/12) - 1 : that will result in ~ .004735

    Finally, the PV is calculated:
    PV = 1500[1 - (1 + I)^(-60)] / I
    That should give you 78184.36

    OK?
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  3. #3
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    Re: Equivilent Cash Price

    Quote Originally Posted by DenisB View Post
    Sorry...but that's way off...

    First, semi-annual rate must be converted to annual equivalent:
    s = (1 + .0575/2)^2

    Then I is calculated as the monthly rate to achieve above:
    I = s^(1/12) - 1 : that will result in ~ .004735

    Finally, the PV is calculated:
    PV = 1500[1 - (1 + I)^(-60)] / I
    That should give you 78184.36

    OK?
    Plus the 60 000 deposit. So the cash price (today) would be 136 184.36.

    (BTW Sharky, you haven't taken into account the fact that the payments and the interest are happening at different times per year.)
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  4. #4
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    Re: Equivilent Cash Price

    Quote Originally Posted by Debsta View Post
    Plus the 60 000 deposit. So the cash price (today) would be 136 184.36.
    138 184.36

    Go stand in the corner, Debsta!
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  5. #5
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    Re: Equivilent Cash Price

    Yeah yeah...it's just a typo. Settle down!
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  6. #6
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    Re: Equivilent Cash Price

    Quote Originally Posted by Debsta View Post
    Yeah yeah...it's just a typo. Settle down!
    You mean "settle down under"?
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