1. R
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    29 Dec '07 00:21
    I did a calculation for I(2) and here are my results.

    1.03{240,000(1.05)^(2) -60,000 + 1.03[240,000(1.05)^(2-1) -60,000 + 1.03[240,000(1.05)^(2-2) - 60,000] ] }

    after simplification I come up with $ 611,121.66 in the bank

    this is after 3 years

    1986 I(0) = $185,400

    1987 I(1) = $377,400

    1988 I(2) = $611,121.66

    I might need to change the formula a bit...... Just in th I(0) the interest isnt compounded till I (1) this changes the number a bit
  2. R
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    29 Dec '07 00:271 edit
    My final solution to this portion of the problem is this

    I(x) = 1.03{240,000(1.05)^(x)-60,000 + 1.03[(fog)(x-1) + 1.03[(fog)(x-2)+1.03[..........+1.03[..........+[(fog)(x-29)] ] ] ] ] }


    My Brain Hurtz😵
  3. R
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    29 Dec '07 03:082 edits
    Originally posted by joe shmo
    My final solution to this portion of the problem is this

    I(x) = 1.03{240,000(1.05)^(x)-60,000 + 1.03[(fog)(x-1) + 1.03[(fog)(x-2)+1.03[..........+1.03[..........+[(fog)(x-29)] ] ] ] ] }


    My Brain Hurtz😵
    I was compelled to find a numerical value

    so i did all 30 iterations with my latest function

    after the total deduction of 1.5 mill

    I come up with about

    Drum roll.........

    $ 18,412,356.34 in the bank in 2016

    congradulations...............your a wealthy man!
  4. Subscribersonhouse
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    29 Dec '07 08:05
    Thats a lot of math! Seems a bit high, I came up with 4 mil with no interest and you came up with over 400% in thirty years. Could that be right? That is an average of 13% per year. How can that be?
  5. R
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    29 Dec '07 16:381 edit
    Originally posted by sonhouse
    Thats a lot of math! Seems a bit high, I came up with 4 mil with no interest and you came up with over 400% in thirty years. Could that be right? That is an average of 13% per year. How can that be?
    it does seem to be far out, but I think it is supposed to catch you offgaurd

    why this problem is difficult to determine the correct answer is because your prinipal is compounding on top of a compounding savings witch compounds at different interest rates

    For logic's sake, chew on this........towards the end of the thirty years around year 27 your wages alone are close to one million dollars a year and your banking almost all of it...

    think of all the exponential values! Like what happens when you raise 2 ^29 (its gigantic) were raising 1.05, but the idea of counter intuition still remains....I have made plenty of errors along the way, but the logic seems solid too me finally

    however, as usual I could be wrong. I'm not a professional math guy.
    all I can hope for is that someone gets interested in your problem that we know, really knows math.

    I put a lot of work into the solution, but it doesm't seem like anyone else is interested....🙁

    Perhaps a personal message to some of the math experts around here will do the trick, I don't know
  6. Subscribersonhouse
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    30 Dec '07 04:062 edits
    Originally posted by joe shmo
    it does seem to be far out, but I think it is supposed to catch you offgaurd

    why this problem is difficult to determine the correct answer is because your prinipal is compounding on top of a compounding savings witch compounds at different interest rates

    For logic's sake, chew on this........towards the end of the thirty years around year 27 your wag s a personal message to some of the math experts around here will do the trick, I don't know
    Well, I did the arithmetic the long hard way, and by the year 2015, the year after the last kid finished university, they ended up with *Rum Droll*
    $18,244,848.45, generating $531,403.35 per year interest after taxes.
    So we are in agreement within 1%. Considering I may have made some arithmetic mistakes after so many hand calculations, (Well not hand, used a calculator), I'd say your formula is pretty darn accurate. I have them living on 60K per year and re-investing the money and by the time they get to age 57, they have 22 million in the bank and they decided to splurge and start spending 600K per year, which, even with that much, the total still goes up by 60K per year, so stays around 22 mil. Not a bad life, eh.
    Doing it by hand only took a couple of hours.
  7. R
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    30 Dec '07 04:422 edits
    Originally posted by sonhouse
    Well, I did the arithmetic the long hard way, and by the year 2015, the year after the last kid finished university, they ended up with *Rum Droll*
    $18,244,848.45, generating $531,403.35 per year interest after taxes.
    So we are in agreement within 1%. Considering I may have made some arithmetic mistakes after so many hand calculations, (Well not hand, us ear, so stays around 22 mil. Not a bad life, eh.
    Doing it by hand only took a couple of hours.
    not a bad Idea!!....now all i have to figure out is how to get a job that pays 240,000 withs a 5% raise each year and Ill be well on my way...😕

    it took me a while also, its pretty much by hand my way as well, it took me about a half hour

    1986 = 180,000 (I wont compound it and add the interest until next year)
    1987 = 1.03[240,000(1.05)^(1) -60,000 + 180,000] = 383,160

    and i just kept on going.........

    who knows, there might be a way to shorten this up, but i bet it extreemly difficult if it's possible....
  8. Subscribersonhouse
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    30 Dec '07 12:342 edits
    Originally posted by joe shmo
    not a bad Idea!!....now all i have to figure out is how to get a job that pays 240,000 withs a 5% raise each year and Ill be well on my way...😕

    it took me a while also, its pretty much by hand my way as well, it took me about a half hour

    1986 = 180,000 (I wont compound it and add the interest until next year)
    1987 = 1.03[240,000(1.05)^(1) -60,000 ...[text shortened]... there might be a way to shorten this up, but i bet it extreemly difficult if it's possible....
    Don't forget, we specified they were making 400,000 before taxes and have 240K AFTER tax money to play with, so "just" making 240,000 per year won't do it. I figured if they were getting a 5% raise each year, the after tax money would go up by 5% also since they would already be at the maximum tax, 38%, rounded to 40%. Now lets see, how to go about making 400K a year.....
    If you cut everything by 90%, supposing you could live on $6,000 per year, and made 40K, and maybe didn't have to put kids through school, you would end up with 1.8 million in the bank and about 50K per year interest so it is really an exercise in the power of savings, eh.
    Savings and frugality. Obviously that last example would be very difficult to keep up, nobody could live on 500 bucks a month in our society anyway. Maybe if you were an ex-pat living in Peru or something.
  9. R
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    30 Dec '07 18:451 edit
    Originally posted by sonhouse
    Don't forget, we specified they were making 400,000 before taxes and have 240K AFTER tax money to play with, so "just" making 240,000 per year won't do it. I figured if they were getting a 5% raise each year, the after tax money would go up by 5% also since they would already be at the maximum tax, 38%, rounded to 40%. Now lets see, how to go about making 4 cks a month in our society anyway. Maybe if you were an ex-pat living in Peru or something.
    My first instinct was that the wages would be different

    Ill do it your way using a version of my last formula:

    [400,000(1.05)^(2) -.40(400,000(1.05)^(2))]

    [441,000 -.40(441,000)]

    [441,000 - 176,400]

    264,600

    That represents your wages in 1988

    My original way comes up with the same results.... and is much shorter

    240,000(1.05)^2 = 264,600

    verbally i don't know why nothing changes, but the numbers don't lie!
  10. Subscribersonhouse
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    01 Jan '08 01:38
    Originally posted by joe shmo
    My first instinct was that the wages would be different

    Ill do it your way using a version of my last formula:

    [400,000(1.05)^(2) -.40(400,000(1.05)^(2))]

    [441,000 -.40(441,000)]

    [441,000 - 176,400]

    264,600

    That represents your wages in 1988

    My original way comes up with the same results.... and is much shorter

    240,000(1.05)^2 = 264,600

    verbally i don't know why nothing changes, but the numbers don't lie!
    Since they are already in the top tax bracket, the 5% increase is linear with before and after tax so the entire series can be done just using the same 5% increase, only on just the after tax portion, ignoring the before tax #'s.
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    02 Jan '08 17:27
    You forgot to mention you need an IQ of 195 to solve this...
  12. Standard memberleisurelysloth
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    04 Jan '08 04:19
    Originally posted by ydmish
    You forgot to mention you need an IQ of 195 to solve this...
    ...or an Excel spreadsheet. 🙄
  13. Standard memberleisurelysloth
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    04 Jan '08 04:25
    Originally posted by PBE6
    Jesus Christ sonhouse, ever hear of the "Enter" key? It splits gigantic paragraphs into more readable chunks. Try it sometime.
    I love the delicate manner in which you convey your concerns, while simultaneously taking great care to avoid any hurt feelings. LMAO! Rec'd.
  14. Subscribercoquette
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    04 Jan '08 05:48
    i can't bellieve i just read this thread.
  15. R
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    04 Jan '08 06:07
    Originally posted by coquette
    i can't bellieve i just read this thread.
    well thankfully its been solved to a certain extent, at least i hope so.......

    However a real problem would have a few more variables i suppose

    oh well,...i enjoyed working this out! I would like all those serious math people to check this out, and see if there is a way to sum the sub-series?

    It would be great to see a simple version of this
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