Raises

Marilyn vos Savant posed this question: Say you're making $10,000 a year. Your boss offers you a choice between a $1,000 raise once a year and a $300 raise every six months. Which do you choose? Marilyn says you should choose the $300 raise. I disagree but I'll lay out Marilyn's math and explanation for you.

Say Marilyn vos Savant and you each makes $10000 a year. Starting Jan. 1, 2001, Marilyn takes the $300 raise every six months and you take the $1000 raise once a year. In the first six months you both make $5000. In the next six months, Marilyn makes $5300 and you make $5000 for a total on the year of $10300 and $10000, respectively.

On Jan. 1, 2002, you both get raises - $300 for her, $1000 for you. Her pay for the next six months is $5600, yours is $5500. On July 1, she gets a raise and you don't; for the next six months, her pay is $5900 and yours is $5500. After two years she's made $21800 and You've made $21000. In the first six months of 1993, Savant makes $6200 and you make $6000, for a grand total of $34000 for her and only $33000 for you.

                       Marilyn vos Savant            You
                 Pay for   Running      Pay for   Running
    Period        period     total       period     total
--------------   -------   -------      -------   -------
2001, 1st half     $5000     $5000        $5000     $5000
      2nd half     $5300    $10300        $5000    $10000
2002, 1st half     $5600    $15900        $5500    $15500
      2nd half     $5900    $21800        $5500    $21000
2003, 1st half     $6200    $28000        $6000    $27000
      2nd half     $6500    $34500        $6000    $33000
2004, 1st half     $6800    $41300        $6500    $39500
      2nd half     $7100    $48400        $6500    $46000

You'll notice that as time goes on, the earnings gap only increases. Can anyone deduce what's wrong with all this? 

Answer:

Given the question as stated, most people would interpret a $300 raise to mean a $300 increase in annual salary--that is, after six months your salary would rise from $10,000 to $10,300 per year. In your first year you'd make $10,150--$5,000 the first six months, $5,150 the second--not the $10,300 Marilyn claims. Under Marilyn's math she's giving herself two $600/year a raises--as reflected in her starting salary for 2002 which is $11,200 (5,600 x 2)--thus her modest $300 raise somehow bolstered her salary by $1200 in a single year. Applying the raise to the yearly salary, there's no way a semiannual $300 raise would beat out an annual $1,000 raise.