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
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Originally posted by joe shmoI was compelled to find a numerical value
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😵
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!
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Originally posted by sonhouseit does seem to be far out, but I think it is supposed to catch you offgaurd
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?
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
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Originally posted by joe shmoWell, 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*
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
$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.
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Originally posted by sonhousenot 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...😕
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.
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....
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Originally posted by joe shmoDon'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.....
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....
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.
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Originally posted by sonhouseMy first instinct was that the wages would be different
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.
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!
Originally posted by joe shmoSince 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.
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!
Originally posted by coquettewell thankfully its been solved to a certain extent, at least i hope so.......
i can't bellieve i just read this thread.
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