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Math Help - Rate of appreciation: the rule?

  1. #1
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    Rate of appreciation: the rule?

    can anyone help me with a rule for rate of appreciation? I have a rule except i dont think im putting it into my calculator right i keep getting overally large numbers.
    Thanks
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  2. #2
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    Quote Originally Posted by xxpink__saltxx View Post
    can anyone help me with a rule for rate of appreciation? I have a rule except i dont think im putting it into my calculator right i keep getting overally large numbers.
    Thanks
    Can you be more specific

    RonL
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    well my question is: the value of a stamp increases from $700 to $1000 in 2 years. What is the rate of appreciation?
    Sorry i was a little late replying

    my formula is: n ^(fv/pv)+1

    n=time
    ^ = square root sign (cant find one on the keyboard)
    fv= future value
    pv=present value

    When i put my above values in i get this: 2^(1000/700)+1 = 3.39

    The answer on my sheet is actually 19.52% p.a.
    How do i get that?
    Last edited by xxpink__saltxx; November 24th 2006 at 03:08 AM.
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    Quote Originally Posted by xxpink__saltxx View Post
    well my question is: the value of a stamp increases from $700 to $1000 in 2 years. What is the rate of appreciation?
    Sorry i was a little late replying

    my formula is: n ^(fv/pv)+1

    n=time
    ^ = square root sign (cant find one on the keyboard)
    fv= future value
    pv=present value

    When i put my above values in i get this: 2^(1000/700)+1 = 3.39

    The answer on my sheet is actually 19.52% p.a.
    How do i get that?
    Are you sure that formula is correct?
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  5. #5
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by xxpink__saltxx View Post
    well my question is: the value of a stamp increases from $700 to $1000 in 2 years. What is the rate of appreciation?
    Sorry i was a little late replying

    my formula is: n ^(fv/pv)+1

    n=time
    ^ = square root sign (cant find one on the keyboard)
    fv= future value
    pv=present value

    When i put my above values in i get this: 2^(1000/700)+1 = 3.39

    The answer on my sheet is actually 19.52% p.a.
    How do i get that?
    I can't get the 19.52% in either event, but is the formula:
    n^{\left ( \frac{fv}{pv} \right ) } + 1

    or

    n^{\left ( \frac{fv}{pv} + 1 \right ) }

    In any event this isn't an equation. What's this expression equal to?

    -Dan
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  6. #6
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    Quote Originally Posted by xxpink__saltxx View Post
    well my question is: the value of a stamp increases from $700 to $1000 in 2 years. What is the rate of appreciation?
    Sorry i was a little late replying

    my formula is: n ^(fv/pv)+1

    n=time
    ^ = square root sign (cant find one on the keyboard)
    fv= future value
    pv=present value

    When i put my above values in i get this: 2^(1000/700)+1 = 3.39

    The answer on my sheet is actually 19.52% p.a.
    How do i get that?
    Hello,

    you wrote: "...my formula is: n ^(fv/pv)+1"

    I understand your explanations that you want to calculate:

    \sqrt [n]{\frac{fv}{pv}}+1

    The 2nd root is the same as the good ol' square-root.

    \sqrt[2]{\frac{1000}{700}}+1 \approx 2.1952286

    Look at the increase: You find 0.1952286 and that's the same as 19.52%.

    By the way: I don't understand what you want to calculate, I can only show you how to get the result.

    EB
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  7. #7
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    Smile

    Quote Originally Posted by xxpink__saltxx View Post
    well my question is: the value of a stamp increases from $700 to $1000 in 2 years. What is the rate of appreciation?
    Sorry i was a little late replying

    my formula is: n ^(fv/pv)+1

    n=time
    ^ = square root sign (cant find one on the keyboard)
    fv= future value
    pv=present value

    When i put my above values in i get this: 2^(1000/700)+1 = 3.39

    The answer on my sheet is actually 19.52% p.a.
    How do i get that?
    Here is one way.

    I don't know your formula but a few play showed it came from the simple formula
    A = P[(1+r)^n]
    where
    A = total amount in n years-----------------your Fv
    P = initial amount, or amount in zero year----your Pv
    r = rate of interest per year------------------your rate of appreciation
    n = number of years

    ------------
    Since it is vacation time, lots of sparetime, let us review how that simple formula was derived.

    0 year:
    Ao = P

    After 1 year:
    A1 = P +P*r = P(1+r)

    After 2 years:
    A2 = P(1+r) + [P(1+r)]*r = [P(1+r)](1+r) = P[(1+r)^2]

    ....After n years:
    An = P[(1+r)^n]

    ----->>> "Ao, A1, A2....An" are read "A sub 0", "A sub 1", "A sub 2"...."A sub n"
    ----------------------------

    So you have
    Fv = (Pv)[(1+r)^n]
    Divide both sides by Pv,
    (Fv)/(Pv) = (1+r)^n
    To isolate r, get the nth roots of both sides,
    [(Fv)/(Pv)]^(1/n) = 1+r
    Hence,
    r = [(Fv)/(Pv)]^(1/n) -1 ---------------(i), it is minus 1.

    Yours is +1, that's why you're getting wrong answers from your calculator.

    So, with n=2,
    r = [1000/700]^(1/2) -1
    r = 1.1952 -1
    r = 0.1952
    r = 19.52 percent ---------------answer.
    Last edited by ticbol; December 30th 2006 at 02:09 PM.
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  8. #8
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by ticbol View Post
    Here is one way.

    I don't know your formula but a few play showed it came from the simple formula
    A = P[(1+r)^n]
    where
    A = total amount in n years-----------------your Fv
    P = initial amount, or amount in zero year----your Pv
    r = rate of interest per year------------------your rate of appreciation
    n = number of years

    ------------
    Since it is vacation time, lots of sparetime, let us review how that simple formula was derived.

    0 year:
    Ao = P

    After 1 year:
    A1 = P +P*r = P(1+r)

    After 2 years:
    A2 = P(1+r) + [P(1+r)]*r = [P(1+r)](1+r) = P[(1+r)^2]

    ....After n years:
    An = P[(1+r)^n]

    ----->>> "Ao, A1, A2....An" are read "A sub 0", "A sub 1", "A sub 2"...."A sub n"
    ----------------------------

    So you have
    Fv = (Pv)[(1+r)^n]
    Divide both sides by Pv,
    (Fv)/(Pv) = (1+r)^n
    To isolate r, get the nth roots of both sides,
    [(Fv)/(Pv)]^(1/n) = 1+r
    Hence,
    r = [(Fv)/(Pv)]^(1/n) -1 ---------------(i), it is minus 1.

    Yours is +1, that's why you're getting wrong answers from your calculator.

    So, with n=2,
    r = [1000/700]^(1/2) -1
    r = 1.1952 -1
    r = 0.1952
    r = 19.52 percent ---------------answer.
    Nicely done!

    -Dan
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