Re: your question dd 10 apr 2004 - sorry for the delay in posting but I only recently discovered your site!!
The question was: (from Marilyn vos Savant etc…)
“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.”
I think you’re wrong. First the question defines the salary as 10000 per year, not 5000 per half year. Secondly, at the start of the second year, the starting salary would be 10600, so in the first 6 months of year 2, you only earn 5300, not 5600 as you state. You only get half of the annual salary in the first six months of each year. Do the math - you’re still worse off.
So whilst in the first year you are better off - after that you’re not. Spreadsheet available if you want to see it!
Second, please include a link to the column you’re referencing in this section, as well as in the Comments on Staff Reports section. Makes it easier for everyone to see what you’re talking about! Like so: http://www.straightdope.com/classics/a3_198.html .
Third, I think (on my reading) that Cecil agrees that your interpretation is the most natural; but he also thinks that Marilyn’s interpretation of the question, while somewhat strained, can also be supported on the wording. And under that interpretation, here analysis is correct. A more precisely-worded statement of the riddle would have been helpful, but she (and Uncle Cecil) can only work with what they’re given …
I wondered about this one myself. I was curious enough to run it through our payroll software with a once yearly $1000 raise and a six-monthly $300 raise. Even correcting for tax and inflation I got the same result. Roughly, the results were the employee was £150 better the first year, £50 worse off the second year, £675 worse off the third year etc.
Can anyone give me a clearer explanation of this? (The tax system used was UK, not US if that makes a difference.)
I’m not sure what you want explained … in your simulation, the $300 semi-annual raise starts out ahead, because it starts kicking in six months sooner. But it’s enough less of a raise that the $1000 annual raise is able to pretty quickly eat up the head start. The alternate interpretation has the semi-annual raise amount being applied to the semi-annual salary (rather than the annual salary), and starts ahead and stays ahead. The minimum semi-annual raise need to beat the $1000 annual raise appears to be around $462 …