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Math Help - Find past value of money? Isn't actually just like finding future value of money

  1. #1
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    Find past value of money? Isn't actually just like finding future value of money

    Say if we were to find the past value of $1 at an interest rate of 5% for the 10 years past today.

    If we were to use the present value formula

    PV = \frac{FV}{(1+i)^n}

    where
    FV=1
    i=0.05
    n=-10

    PV = \frac{1}{(1+0.05)^{-10}}
    PV = \frac{1}{(1.05)^{-10}}
    PV = (1.05)^{10}
    PV = 1.62889462677744140625

    It seems like the past value of $1 is kind of like future value of $1

    Does this make sense?

    To me it kind of does, since a dollar in hand today is worth less than a dollar we had 10 years ago

    Would someone here comment on these findings
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  2. #2
    MHF Contributor alexmahone's Avatar
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    Quote Originally Posted by dexteronline View Post
    Say if we were to find the past value of $1 at an interest rate of 5% for the 10 years past today.

    If we were to use the present value formula

    PV = \frac{FV}{(1+i)^n}

    where
    FV=1
    i=0.05
    n=-10

    PV = \frac{1}{(1+0.05)^{-10}}
    PV = \frac{1}{(1.05)^{-10}}
    PV = (1.05)^{10}
    PV = 1.62889462677744140625

    It seems like the past value of $1 is kind of like future value of $1

    Does this make sense?

    To me it kind of does, since a dollar in hand today is worth less than a dollar we had 10 years ago

    Would someone here comment on these findings
    n=10, not -10.
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  3. #3
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    Quote Originally Posted by alexmahone View Post
    n=10, not -10.
    My attempt was to find past value of money thus I used -10 for the 10th year in past from today. If I were to use 10 that will give us the present value of money for the 10th year in the future.

    If I am attempting it wrong, may you suggest how we would go about finding PAST value of money.
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  4. #4
    MHF Contributor alexmahone's Avatar
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    Quote Originally Posted by dexteronline View Post
    If I were to use 10 that will give us the present value of money for the 10th year in the future.
    Let PV be the value 10 years back. Then FV is the future value of money relative to 10 years back; so it is the present value.
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  5. #5
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    Quote Originally Posted by alexmahone View Post
    Let PV be the value 10 years back. Then FV is the future value of money relative to 10 years back; so it is the present value.
    Thanks for the reply
    Help me out with this

    a) What was $1 worth on Jan 5, 2001 if interest rate is 5%

    b) What will be the value of $1 on Jan 5, 2021 if interest rate is 5%
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  6. #6
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    Quote Originally Posted by dexteronline View Post
    a) What was $1 worth on Jan 5, 2001 if interest rate is 5%
    b) What will be the value of $1 on Jan 5, 2021 if interest rate is 5%
    a) 1.05^(-10)
    b) 1.05^10
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