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Salary Riddle.

Former MemberFormer Member Posts: 1,876,323 The Mix Honorary Guru
You work for a company and your chef pays you 10.000 pounds.
Now you have two options:
1. Take a raise of 1000 pounds a year
or
2. Take a raise of 250 pounds every half year

which one will you chose?

Comments

  • Former MemberFormer Member Posts: 1,876,323 The Mix Honorary Guru
    I suppose there will be a trick to this but I will go with the obvious answer, which is #1. :rolleyes:
  • SkiveSkive Posts: 15,282 Skive's The Limit
    No1

    no brainer
    Weekender Offender 
  • Former MemberFormer Member Posts: 1,876,323 The Mix Honorary Guru
    Well, the obvious answer is #1, that's right, who wouldn't chose that? In reality tho, the guy who picks the 250 half yearly will earn more. It's pretty complicated and I was twisting my gyruses for hours yesterday, but I'll give it a go.

    Look at the attachment. the left coloums are the +250/ ½ year guy, the right ones the +1000/year
    In the first semester (half year), both earn 5000.
    then, the +250 each half year dude gets a raise.
    In the second semester he earns 5250 and gets another raise of 250, the 1000 a year guy earns 5000 again.
    From the beginning of the third semester, the 250 half yearly guy will earn 5500 this semester. Since we are looking at this half-yearly, the 1000 a year guy earns exactly half his salary in one semester, which will be 5500. (10000 + 1000 raise halfed)

    See it already? Look at the chart in the index.
    in the column "sum of earned cash", the 1000 a year guy has always
    10000 1st year
    11000 2nd year
    12000 3rd year

    But every year the 250 half a year guy is 250 in advance.
    This is no trick on numbers. I know it's very confusing and seems to repel human logic, but maths prove it pretty much.

    I try to make a more transparent example. According to your theory a guy who gets a 1000 raise a year should have as much money as a guy who gets 500 each half-year. Well, the 1000 a year works for the same basis salary for one year, while the 500-dude works for +500 after already one semester.

    Look at the graph too. The sum of the area of the pillars of one colour is the amount of cash any of these guys have at every given moment. you can see, that one semester the 250-guy is +250 in advance, and the other semester they are even. Every year the 250-guy has +250 pounds.
  • JsTJsT Posts: 18,268 Skive's The Limit
    No - still doesn't make any sense.
  • Former MemberFormer Member Posts: 1,876,323 The Mix Honorary Guru
    Your figures I think are assuming that you actually earn your raise in the period before its granted, which gives the more frequent raise-earner an advantage.

    I think a more accurate representation is to show how much each person gets as their raise, because their base salary was the same (10000) at the start point, so you're really only concerned with how much extra each person gets. Done this way you can see the big raise winning -

    250 1000
    year 0 0 0
    year 0.5 250 0
    year 1 250 1000
    year 1.5 250 0
    year 2 250 1000
    year 2.5 250 0
    year 3 250 1000

    total 1500 3000

    After three years the 250 raiser has earnt his 10000 + 1500 extra, the other guy has earnt 3000 extra. (Actually neither of them has earnt that yet until the next year, but that factor is the same for both)
  • Former MemberFormer Member Posts: 1,876,323 The Mix Honorary Guru
    Mist wrote: »
    Your figures I think are assuming that you actually earn your raise in the period before its granted, which gives the more frequent raise-earner an advantage.

    I think a more accurate representation is to show how much each person gets as their raise, because their base salary was the same (10000) at the start point, so you're really only concerned with how much extra each person gets. Done this way you can see the big raise winning -

    250 1000
    year 0 0 0
    year 0.5 250 0
    year 1 250 1000
    year 1.5 250 0
    year 2 250 1000
    year 2.5 250 0
    year 3 250 1000

    total 1500 3000

    After three years the 250 raiser has earnt his 10000 + 1500 extra, the other guy has earnt 3000 extra. (Actually neither of them has earnt that yet until the next year, but that factor is the same for both)

    There is no mistake in my calculations. No, I am getting the raise after it's granted. you have to consider only the money that's earned not the raise. Just add all the money together that's earned.
    year 0 to 0,5 : both earn 0 pounds
    year 0,5 to 1 : 250-guy earns 250, 1000-guy earns 0
    year 1 to 1,5 : 250-guy has 250 from last semester + 500 (salary of former semester + raise of 250) = 750 pounds. 1000-guy earns 500 (he will earn 1000 because of his raise over the whole year, which makes 500 a semester)
    year 1,5 to 2: 250-guy has earned 750 pounds before and his salary is 750 (500 from last semester + 250 raise), amounts 1500 pounds.
    1000-guy doesn't get his second raise yet, in the second semester of this year he earns another 500, which amounts to 1000 now. (1000 a year).

    We have year 2 now, and 250 guy is 500 in advance, like I said 250 a year more cash. I have a documentation of this and a finance mathematician calculates it through. Unfortunately it's in german, if you are still interested I will provide the link. There is no mistake in it.

    First semester nobody gets a raise, after one semester of work, 250-guy gets paid +250 for the following semester. after one year 1000-guy gets paid +1000 for the following year.

    Yeah, it doesn't add up with common sense, but it's true. If you have the time, a friend, and enough M&Ms try it out. I've tried to refute it for hours, then I told my father about it and he tried it for some time, but in the end the numbers don't lie.



    Maybe an even more transparent example shows this.
    2 guys earn 0 pounds, chef says: either take 365 pounds raise a year, or take 1 pound raise every day.
    option one provides +365 pounds every year, which is 0 pounds first year, 365 pounds after second year (which equals 1 pound for a day).
    option two provides 0 pounds first day
    1 pound the second day
    2 pounds the third day
    3 pounds the forth day
    4 pounds the 5th day
    5 poudns the 6th day. Every day a raise +1 pound. and now add all he every earned together.

    5+4+3+2+1+0 = 15 pounds after 6 days, which is clearly more than 1 pound a day.
    The more often the progression the more you cash you have in your wallet in every infinitesimal period.
  • Former MemberFormer Member Posts: 1,876,323 The Mix Honorary Guru
    I can't help but think that you're over complicating this...
  • Former MemberFormer Member Posts: 1,876,323 The Mix Honorary Guru
    hahah you sick cunt who the fuck cares
  • Former MemberFormer Member Posts: 1,876,323 The Mix Honorary Guru
    Mist wrote: »
    Your figures I think are assuming that you actually earn your raise in the period before its granted, which gives the more frequent raise-earner an advantage.

    Can you explain this? The +250/half-year-guy, works the first semester for original salary, then becomes his raise and works the second semester for 250 pounds more. This is what I used based on my calculations.
    After three years the 250 raiser has earnt his 10000 + 1500 extra, the other guy has earnt 3000 extra. (Actually neither of them has earnt that yet until the next year, but that factor is the same for both)

    the +1500 extra is wrong. His raises would have reached +1500 cash by now, which means he would earn an additional 1500 for the next semester alone.
    In reality he made
    +0 in first semester. The day which separates 1st and second semester he gets his raise and will earn +250 for the next work-semester
    +250 after the second semester
    +500 in third = 750 (250 he earned last semester + salary: 500 = 750)
    750 (he earned all in all in the former semesters) + salary: 750 = 1500

    --> he earned 1500 extra at the end of third semester.

    Maybe we have a different understanding of when the new raise is paid out?
    the problem is covered here and a video here. Unfortunately they are both in german.
  • Former MemberFormer Member Posts: 1,876,323 The Mix Honorary Guru
    There's a video to explain this... :sour:
  • Former MemberFormer Member Posts: 1,876,323 The Mix Honorary Guru
    Isn't this just another take on the problem: A man and a tortoise are having a race in which the tortoise is given a head start. The man runs to where the tortoise was but the tortoise has always moved on a bit more; the man can never catch up. It appears to make sense - if you screw your eyes up and have a beer - but clearly the model you're using to solve the problem is broken.
  • Former MemberFormer Member Posts: 1,876,323 The Mix Honorary Guru
    Take a raise of £1000 a year = One raise of £1000 a year. No more raises after that.

    Take a raise of £250 every half year = A raise of £250 every 6 months, presumably until you quit.

    So the answer would depend on how long you're planning on working there.

    That's the way I read it.
  • Former MemberFormer Member Posts: 1,876,323 The Mix Honorary Guru
    Problem is that if someone gets a raise of $250 at the 6 month point, he doesnt earn an extra $250 in that 6 months, thats a rate of $250 a year, so in that half year he will only have earned an extra $125 dollars
  • Former MemberFormer Member Posts: 1,876,323 The Mix Honorary Guru
    You obviously don't work hard enough if you have time to work out all of that :yum::D
  • Former MemberFormer Member Posts: 1,876,323 The Mix Honorary Guru
    Take a raise of £1000 a year = One raise of £1000 a year. No more raises after that.


    I thought that, if you're going to be there a long time 250 every 6 months will work out more BUT '£1000 a year' implies every year otherwise it should read a raise of £1000.
  • Former MemberFormer Member Posts: 1,876,323 The Mix Honorary Guru
    StrubbleS wrote: »
    Well, the obvious answer is #1, that's right, who wouldn't chose that? In reality tho, the guy who picks the 250 half yearly will earn more. It's pretty complicated and I was twisting my gyruses for hours yesterday, but I'll give it a go.

    Look at the attachment. the left coloums are the +250/ ½ year guy, the right ones the +1000/year
    In the first semester (half year), both earn 5000.
    then, the +250 each half year dude gets a raise.
    In the second semester he earns 5250 and gets another raise of 250, the 1000 a year guy earns 5000 again.
    From the beginning of the third semester, the 250 half yearly guy will earn 5500 this semester. Since we are looking at this half-yearly, the 1000 a year guy earns exactly half his salary in one semester, which will be 5500. (10000 + 1000 raise halfed)

    See it already? Look at the chart in the index.
    in the column "sum of earned cash", the 1000 a year guy has always
    10000 1st year
    11000 2nd year
    12000 3rd year

    But every year the 250 half a year guy is 250 in advance.
    This is no trick on numbers. I know it's very confusing and seems to repel human logic, but maths prove it pretty much.

    I try to make a more transparent example. According to your theory a guy who gets a 1000 raise a year should have as much money as a guy who gets 500 each half-year. Well, the 1000 a year works for the same basis salary for one year, while the 500-dude works for +500 after already one semester.

    Look at the graph too. The sum of the area of the pillars of one colour is the amount of cash any of these guys have at every given moment. you can see, that one semester the 250-guy is +250 in advance, and the other semester they are even. Every year the 250-guy has +250 pounds.


    Yes but when a guy gets a raise of $250 a year at the 6 month point he's only earned an extra $125 dollars, as the $250 a year raise equates to what he would earn over a year.
  • Former MemberFormer Member Posts: 1,876,323 The Mix Honorary Guru
    Over 5 years the $1,000 a year rise will always beat the $250 every 6 months rise.

    I have shown on the attachment how this happens, when it has been tried before, the OP has assumed that when the worker gets a $250 ride on the 6 month point, that they are going to earn an extra $250 in that 6 months, which if you earnt an extra $250 in 6 months would actually relate to a yearly rise of $500 which isnt the case.

    I have broken down the pay frames into slots of 6 months as the OP had done, and worked out how much cash the two workers would have earned over 5 years, taking into account how much they would earn in each 6 monthly slot, acording to their yearly rate of pay at that given 6 month period.

    In each 6 month period i have taken their yearly rate of pay at that given period, and divided it by 2.
  • Former MemberFormer Member Posts: 1,876,323 The Mix Honorary Guru
    I will not go into the solution in detail, because I can't make it any more precise as I have already done. And all I can do is repeat myself for every person who sees this thread and tries to calculate it through on their own, but clearly, I'm not going to do that.

    Mr G: It says 250 raise each semester.

    That means first semester of work: no raise, just usual salary of "x/2" (where x is the salary for a whole year)
    A raise of 250/semester means, at the moment of the raise (so the 1.July (exactly after half a year)) you work for x/2+250 in total for the next semester. You can pay out the 250 at any rate, mabye 250/6, for each month of the semester, but it's +250 a half-year, period. That's how I stated it in the original post. If there are problems or misconceptions with semantics or syntactics I apologize.
  • Former MemberFormer Member Posts: 1,876,323 The Mix Honorary Guru
    StrubbleS wrote: »
    You work for a company and your chef pays you 10.000 pounds.
    Now you have two options:
    1. Take a raise of 1000 pounds a year
    or
    2. Take a raise of 250 pounds every half year

    which one will you chose?

    raise of 250 every half year

    means that at the 0.5 year point your yearly pay goes up to 10250, but you cant earn the whole 250, as your only then working 6 months in that first year with a raise.

    The pictures you posted earlier, you said they got a raise at the 0.5year point, and shows that they earned an extra 250 in that second 6 month period. That would equate to a yearly rise of 500.

    You need to look at my post above and look at the attachment and tell me where i have gone wrong. I have shown what their year rate of pay is at any gievn time, and how it changes every 6 months, and how much they earn in every 6 month period.

    Your original calculation as shown on the attachment on this post is wrong, if you get a pay rise of 500 you would earn an extra 250 in a 6 month period, but as you state in your first post, its a 250 raise, which equates to an extra 125 every 6 months, every time they got a raise.

    Show me where my maths is wrong.
  • Former MemberFormer Member Posts: 1,876,323 The Mix Honorary Guru
    StrubbleS wrote: »
    I will not go into the solution in detail, because I can't make it any more precise as I have already done. And all I can do is repeat myself for every person who sees this thread and tries to calculate it through on their own, but clearly, I'm not going to do that.

    Mr G: It says 250 raise each semester.

    That means first semester of work: no raise, just usual salary of "x/2" (where x is the salary for a whole year)
    A raise of 250/semester means, at the moment of the raise (so the 1.July (exactly after half a year)) you work for x/2+250 in total for the next semester. You can pay out the 250 at any rate, mabye 250/6, for each month of the semester, but it's +250 a half-year, period. That's how I stated it in the original post. If there are problems or misconceptions with semantics or syntactics I apologize.

    Ahh i have figured it out, the question itself is misleading, when it says theres a 250 rise every semester, it means actual monetary rise of 250 in that 6 months (perhaps) which would equate to a payrise of 500 annually, i think thats what the question was perhaps aiming at.

    Though the reason I, and several other people have failed to get our heads around it, is that when we get a payrise, we dont get $x extrara over a certain period, our yearly rate goes up, which doesnt mean we would get an extra 250 in a 6 month period for having a 250 rise per semester, that suggests that the yearly rate of pay goes up by 250. Thats how the real world works.
  • Former MemberFormer Member Posts: 1,876,323 The Mix Honorary Guru
    :banghead:

    It made sense when you used the little numbers. I think I will just be happy with having understood that much!
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