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Math Help - Tax Rate changes after sometime, how to find it?

  1. #1
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    Tax Rate changes after sometime, how to find it?

    Hi,

    I've been trying to solve the following problem:


    A seller deposited $8.000, 1 year and 4 months after, he raised $8.480.
    Knowing that, some time after the deposite, the anual tax rate passed from 4% to 6%, determinate how much time it took for the tax change to happen ?

    This is what I've tryed (and a couple of 3 diferent methods, similar to this one):

    I know that, 8.480 = 8.000(1 + 16/12 * i)

    Interest = i

    so, I wrote the following equation for the given word problem

    ( i1 + i2 ) + c1 = c1( 1 + 16/12 * i )

    I started by finding i wish gives me i = 0,04466 ~ 0,045

    I know that,

    i1 + i2 = 480 , from a total of 16 months

    i1 = 8.000 + [ (16-n1)/12 ] * 0,04

    i2 = 8.000 + [ (16-n2)/12 ] * 0,06

    It gave me,

    i1 = (320n1)/12

    and

    i2 = (480n2)/12

    further I've picked from i1 + i2 = 480

    the following result,

    [(320n1)/12] + [(480n2)/12] = 480

    n1 = 216 - 480n2

    I was thinking that, if I used this values I could get the answer by

    (8.000 * [(216-480n2)/12] * 0,04) + (8000 * (n2/12) * 0,06) + 8.000 = 8.480

    But it does not... probably I've got lots of errors and I'm not that good in math, but I do my best

    Any sugestion is appreciated!

    Thanks for your atention
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  2. #2
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    I've tryed it a couple of times more, without success.

    Unfortunately the steps above, that I pasted have lots of errors, but the way is done or I've used is that one
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  3. #3
    MHF Contributor
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    Quote Originally Posted by heldrida View Post
    A seller deposited $8.000, 1 year and 4 months after, he raised $8.480.
    Knowing that, some time after the deposite, the anual tax rate passed from 4% to 6% .....
    In future:
    Please post (as example) $8.000 this way: $8,000
    Please use INTEREST rate, not tax rate.
    Please use CHANGED (not passed) and ACCUMULATED (not raised).

    Here's a much simpler way:
    t = time = 1+1/3 year = 4/3 year
    x = time at 4%

    8000(.04x) + 8000(.06(4/3 - x)) = 480
    .04x + .06(4/3 - x) = 480/8000

    I'm sure you can finish it
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