Marilyn is completely wrong. Try making her the same offer and see which one she accepts.
You get a $300 pay raise at the end of six months. Then you get a $300 pay raise at the end of the year. Net increase: $600
OR
You get a $1,000 pay raise at the end of the year. Net increase: $1,000.
At the end of the first year you are $400 behind with the six-month scheme. You stay behind and fall further behind as long as you keep the scheme going.
Cecil says, “A semiannual raise of $300 is an annual increase of $600, and if you have two such increases per year your annualized salary hike is $1,200.” Also wrong. Your annualized pay increase is $600.
Yes, yes, you’re very smart. Now answer this: does “a $300 pay raise” refer to $300 annually, or $300 per six months (which is the period in question)? And why?
Powers &8^]
No, you are not $400 behind at the end the first year. You got $300 over base salary mid-year. So, that’s +300 more. Then at the end of the year, you get a $600 raise which is $600 added to the $300 you already got mid-year. That’s $900 raise at the end of the first year. That’s only $100 behind.
Now, if you keep remembering to keep a running total of what they received previously, the one with the six-month $300 winds up with more.
Year 1: 5300+5600=10900 vs. 10000+1000=11000
Year 2: 5900+6200=12300 vs. 11000+1000=12000
Year 3: 6500+6800=13300 vs. 12000+1000=13000
Year 4: 7100+7400=14500 vs. 13000+1000=14000
You lose in the first year, but are better off thereafter.
Note that the conditions specified that the pay raise was at the END of the 6-month or 1-year period and that it was not paid as a bonus. So if the starting salary was $10,000 annually ($5000 semi-annually) and they took the semi-annual raise, that meant they worked the first six months at the original $5000 rate and for the second six months at the $5300 rate. If they took the $1000 raise at the END of the first year (and it was not paid out retroactively or as a lump sum), that meant they worked for $10,000 for the whole first year, but earned $11,000 for the second year.
Year 1: 5000+5300=10300 vs. 10000+0000=10000
Year 2: 5600+5900=11500 vs. 10000+1000=11000
Year 3: 6200+6500=12700 vs. 11000+1000=12000
Year 4: 6800+7100=13900 vs. 12000+1000=13000
The question is, do you interpret the $300 raise as being $300 per year or $300 per half-year? The above calculation assumes it is $300 per half-year. But given that the original salary was stated as an annual amount ($10,000 per year), it seems inconsistent to assume that the raise would be stated as a semi-annual amount. The original question does not clarify this.
There are no specific words in the question to indicate that the raises are treated differently: look at each phrase and try to find a point of differentiation:
The only points of differentiation in the words as written is when the raises occur, there is no difference in word choice describing the raise and therefore no justification for treating the phrases differently. For all we know, it could be hourly raise. But what we do know is that the manner of raise is no different between scenarios, not on the basis of any actual words present.
An important piece of information that is needed to answer the question is how long you will be working there.
If you work there only one year then the $300 raise every 6 months is better.
Even with the interpretation that your 6 month salary goes up $150 every 6 months.
You get $10,150 with the $300 raise and only $10,000 with the $10,000 raise
But suppose your 6 month salary goes up by $300 every 6 months as Marilyn interpreted it.
You will make more money with the the $300 raise as long as you work there less than 8 years. But if you work there longer than 8 years the $1000 raise is better
I calculated it all in Excel below
The 2nd and 4th columns show the money made in each 6 month period with both types of raises.
The 3rd and 5th columns show the cumulative salary made for each type of raise.
At 8 years you break even. After that, the $1000 raise gives you more total money.
You messed up the fourth column.
Beginning at year 4.5, you started giving him $500 semi-annual raises instead of $1000 annual raises.
If you don’t know what I’m saying, read down the fourth column and notice the pattern: The number goes up by $500 every second entry, then it suddenly starts going up by $500 for every entry.
The patterns listed above are not correct. Let’s call the $1,000 annual raise “Plan A” and the $300 every six months raise “Plan B”.
End of first six months Plan B ahead $300
End of second six months Plan A ahead $400
End of third six months Plan A ahead $100
End of fourth six months Plan A ahead $800
End of fifth six months Plan A ahead $500
So the six-month pattern for Plan A is -$300, +$400, +$100, +$800, +$500, +$1,200, etc. Basically, -$300, +$700 repeating.
And semantics play a part in many word problems, but in Marilyn’s explanation she claimed that Plan B put you ahead by a specific number of dollars. That shows that her intent was to answer which plan was better financially. So her answer is wrong by her own criterium.
I’ve already told you above that is incorrect. At the end of the second six months plan A is only ahead $100. Plan B got $300 over base salary at the end of the first six months and then in addition to the $300 already received another $600 at the end of the second six months.
Folks, here’s pro-tip for presenting tables in vBulletin: use the “code” feature. It will preserve formatting spaces and you can use a fixed width font.
And as the corrected numbers show, you stay ahead with an increase of $300 every six months.
“$1000 raise at the end of one year” is pretty straightforward, because your salary is stated as an annual salary. It’s correlating annual numbers to annual numbers, and so “you get $1000 more the next year”.
The ambiguity comes from “$300 raise at the end of each six months”. To many people, that reads “you get $300 more every six months”. That’s the interpetation that Marilyn uses and how that method comes out ahead.
But you point out that the original salary was stated as an annual salary, so the raise amount should be stated in the same base. Nonsense, where does it say the $300 is an annual increase? It says you get $300 raise each six months.
That’s because people are not machines, and change their points of reference on a whim, in the middle of a sentence, without a clear declaration that’s what they’re doing. It takes contextual interpretation to understand the intent. And that’s also part of why we often have miscommunications, and both parties adamantly believe they are right and the other person is wrong on a conversation both participated in.
If I were to receive an offer like that, I would clarify what “$300 raise each six months” means. Because I could totally see an unscrupulous boss make that offer, with his intention being “I will increase your annual salary $300 each six months”, which makes it only $150 more for the six month period, but hoping I’ll take it as the $300 for the six month period and take that deal.
Doing the numbers for the $150 more each six months interpretation:
Exactly. And Marilyn, in that ancient column, defines things in a way that almost nobody else ever does to come up with her absurd answer.
If you’re making a salary of $10,000 a year, you can think of it if you want as earning a salary of $5000 per demiyear, but no one ever does. And on whatever official piece of paper, Word document, or whatever sitting in HR’s paper or computer files that defines your salary, it says “$10,000 per year.” When they give you a raise, they’re going to cross out that ‘10,000’ and replace it with the new amount, but they’re not going to cross out the ‘year’ and replace it with a new time period, regardless of the frequency of the raises.
Marilyn’s answer comes from an alternate universe where the frequency of the raises also determines the time period over which your salary is defined. And it’s accurate in that universe! Just not in this one.
That’s bullshit. I gave a clear description of how the wording is ambiguous, and how it could easily be interpreted to mean you get an additional $300 every six months.
Yes, but what number are they going to write in? English doesn’t work like computer code. When someone says “I’ll give you a $300 raise every six months”, that sounds an awful like “I’ll give you an additional $300 every 6 months”, not “I’ll give you an additional $150 every 6 months”.
No, Marilyn’s answer comes from a universe where English can be ambiguous and people are not computers.
Life among the befuddled. There is no ambiguity to the question. It’s a $300 raise every six months or a year-end raise of $1,000 each year. No matter how you slice it the $1,000 every year is a better deal. And I stand by my pattern for Plan A compared to Plan B. In six month increments the pattern is -$300, +$700 repeating.
What is a mystery is how Marilyn can say that Plan B puts you “ahead” by a certain number of dollars. The only time Plan B is ahead is between the end of month six and the end of month twelve.