You can not figure this out by averaging raises. The raises keep increasing which keeps changing the average CUMULATIVE raise over time. The accumulated raises increase arithmetically while time increases linearly.
I agree that the typical interpretation would be that the $300 raise is to your annual base rate.
But you can’t simply declare that a specific example must be the typical interpretation when other interpretations are possible.
We were given this information: “Suppose you make $10,000 a year. Your boss offers you a choice: You can have a $1,000 raise (not a bonus) at the end of each year, or you can have a $300 raise at the end of each six months. Which do you choose?” Marilyn says you should choose the $300 raise. “At the end of one year,” she says, “you’d be ahead $300; at the end of three years, $700; and at the end of five years, $1,100.” So in this example, we are given information that makes it clear we’re using the interpretation that a six month pay raise applies to your semi-annual base rate. If you use the annual base rate interpretation, it wouldn’t produce the results you’re given.
It’s the difference between “I don’t have all the information so I’m going to use typical assumptions to derive the facts I need from the information I have” and “I am going to apply typical assumptions to the information I have and throw out any facts that don’t conform to my assumptions”.
What country are you in?
Insufficient, in practice. My mother-in-law lives in a “European” building in New York City, and I’ve encountered “American” buildings in London. Not to mention the occasional supernumerary mezzanine level, or cliffside buildings where the ground entrance may be on the 5th or even the 18th floor.
This has me baffled. Getting passed the semantics and assuming the question is as Marilyn interpereted it, I still don’t understand it. Like the OP, my mind wants to say that $300 + $300 is a yearly increase of $600, but from looking at the math I can see that it’s really $1200. My question is WHY? Is there some simple explanation *in english *that will enable me to wrap my feeble mind around this? Where is that extra “times 2” coming from?
My mind is further blown by realizing that quarterly $100 raises are an even better deal ($1600 raise anually).
Yes, but that wasn’t the question that was asked. The question was simply which is a better deal - whether it’s one penny or a billion dollars better doesn’t impact the answer to the question.
If you got a raise on Jul 1, your base salary would go from $10,000 to $10,300. So you would earn $5000 Jan 1 - Jun 30 ($10,000 / 2) and $5125 Jul 1 - Dec 31 ($10,300 / 2), for a total of $10,125.
People are interpreting that to mean they would get $300 more over half a year (ie earn $10,300 from Jul 1 to Dec 31), which is essentially a $600 raise. Two $600 raises = $1200.
A $1000 raise over a twelve month period is $83.33 a month. A $300 raise over a six month period is $50 a month. Two $300 raises like that adds up to $100 a month.
The “times 2” is because if you’re getting paid a certain amount in a six month period, you’ll collect it twice in a year.
In the context of communication among native English speakers, I daresay that a poll of 1,000 random respondents would be confused by the phrase “semiannual annual pay raise”.
I agree that many people would hear “$300 pay raise at the end of each six months” to mean they will get $300 more for that six month period, not that they will get $150 more for that six month period.
No, you just have to read/hear “$300 pay raise at the end of each six months” and think “that means I get $300 more each six month period”. They’re not associating “pay raise” with the previously stated annual base salary rate of $10,000 per year, they are associating it with “every six months”.
And yet I tell you it is how I understood the question.
But “raise” is an ambiguous term. In this case, the “$300 raise” is paired with the words “every six months”, and not anywhere near the words “annual salary”.
I congratulate you on reevaluating your position and admitting your error.
Jamicat, I already posted all the numbers for comparison in post 18, conveniently in table form. You can see what happens if you get $150 more for each 6 month period, $300 more for each 6 month period, or $1000 more for each year. You can see the 6 month pay, the accumulation for each year, and the total accummulation.
You can easily see that the $150 case lags behind but the $300 is ahead of the $1000 case.
Okay, I think I finally parsed what you are saying. You don’t care that the word said was “annual”, you care that the second statement doesn’t appear to you to state a different period than the first rate is stated.
To which I can only point out that “$300 raise for every six months” associates $300 with six months rather than with “annual salary”. “Raise” means I’m getting paid more. How much more? $300 each six months.
Whereas you and others are arguing the correct interpretation should be “$300 added to your $10,000 per year base salary every 6 months”.
Irish-What exactly is the other interpretation?
Twelve in the U.S., 14 in the UK.
Powers &8^]
You’re applying that “six month period” twice, even though it is only said once:
If it was a $300/six months raise every six months, it should have been mentioned twice, like I just did.
I don’t have to explicitly say $300/year raise every six months to get the reasonable interpretation of the raise being for the annual salary because that context was set in the previous sentence: “Suppose you make $10,000 a year”.
How many stairways are there between the floors? Do you mean there are two separate stairways, each of which has one flight of stairs per floor? Or is there just one stairway with two flights between each pair of floors?
How are the floors numbered? G, 1, 2, …, 7 or G, 2, 3, …, 7 or some other way? Which floor do you consider the ground floor?
He was channeling Marilyn. So he means two stairways, each with two flights of stairs, for a total of 24. Ha ha, you all lose. 
There’s the interpretation that you make $10,150 the first year and the interpretation that you make $10,300 the first year. One interpretation says you add $300 to the $10,000 per year salary each six months, the other interpretation is you add $300 to what you make each six months, which is $5000 for the base period.
People are not computers. We don’t always hear what the other person intended.
Personally, I think you are being redundant. If it’s a $300/six months raise, that tells me you are getting $300 every six months. How often should that be applied except every 6 months? Applying it annually wouldn’t make sense, that would be a $600 annual raise. Applying it every month wouldn’t make sense, that would be a $50 raise every month. Changing the designation of when it’s awarded affects accummulation rate. $300 raise each 6 months tells me I get $300 more each six month period, not $150 more each 6 month period.
I’m not arguing your interpretation is invalid. I’m not even arguing your interpretation is not the intended one. I’m arguing that many people will read it with the interpretation I am giving. I am arguing that it is ambiguous.
And yet I think you do have to say $300/year raise or else it sounds like you mean an additional $300 every six months. It’s association by proximity. Ambiguity results when people approach the same words with different default assumptions.
The statement “$300 raise” is missing the raise period. You supply the default assumption it is added to the previous sentence where it is stated your base salary on an annual basis. I supply the default assumption it is in the same sentence where the next words say “each six months”. If the original statement said “annual raise” there would not be ambiguity.
However, I expect many people would be confused by that. “Wait, a $300 annual raise, but applied every six months? What? So is that like $300 every six months? No? It’s $150 each six months? Well why didn’t you just say that?”
Everyone still needs to stop confusing the rate of raise (whether annual or semiannual) with the rate of accumulated raise. Each period that goes by, your extra income from raises increases linearly, e.g,: 1,000; 2,000; 3,000; 4,000; etc… or its 300; 600; 900; 1,200; etc…
Your rate of accumulated raises is your current rate of raise (e.g., $4,000) PLUS all the previous raises: 3,000 + 2,000 + 1,000, which is $10,000 in raises, not the current $4,000 raise for that period. The accumulated raises increases arithmetically, therefore, you can not average out your cumulative raises (increasing arithmetically) over time (increasing linearly) because that ratio will be ever-changing over time.
No argument. I never said or implied otherwise.
The first requirement, to answer the puzzle, is to resolve the ambiguity. You get a different answer for the two most obvious interpretations. Regardless, when ambiguity rears its ugly head in reality, the result is usually based on how someone goes about handling the numbers (filling in boxes). Someone above said that a self-serving employer would twist the meaning to their benefit. Perhaps, but that same interpretation is what I would expect the vast majority of HR workers to use, without any prodding from the bean counters or any desire to reduce the company’s burden. Not that this bears on the “correct” answer to the puzzle, since there isn’t one, as stated.
Of course, the right way to ask is “What floor is the ground floor?” I remember a number of buildings in Wellington NZ where the ground floor was on the 5th floor on one side, and the 1st (or 0th) on the other. In that case, you’d have to ask “Front or back?” as well.
You said
My point is that it DOES matter whether the raise is based on the hourly, monthly, semi-annual, or annual pay. A $300 raise on your hourly pay is a much bigger raise than a $300 raise on your annual pay. QED. But I see now what you meant, thanks to Irishman. The problem here is that we’re being imprecise in our speech. “The period the raise covers” can be interpreted two ways. It can mean the period over which the raise happens to be in effect, or the term by which the raise is applied.
I think we all have that covered, thank.
The problem with this statement is that nobody is questioning how Marilyn got her answer, we are questioning whether or not her interpretation of the problem is correct. Your reasoning is circular. You are using the fact that Marilyn got the answer she did as evidence that her interpretation of the problem is correct.