A Straight Dope Classic from Cecil's Storehouse of Human Knowledge

What's better, a $1,000 raise each year, or a $300 raise every six months?

April 10, 1992

Dear Cecil:

Marilyn vos Savant recently answered the following question in her column in Parade magazine:

"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."

Could you please double check Marilyn's answer? I don't see how she comes up with these numbers.

Cecil replies:

I shouldn't do this, but I can't resist. Not that you're going to catch me saying Marilyn vos Savant is wrong. On the contrary, her response is 100 percent correct. It's just not necessarily the answer to the question she was asked.

Given the question as stated, many 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. Under that interpretation there's no way a semiannual $300 raise would beat out an annual $1,000 raise.

But that's not what Marilyn has in mind. She interprets the question this way: Would you rather have your $10,000 annual salary increased $1,000 each year, or your $5,000 half-year salary increased $300 every six months?

Put that way, the correct choice is the $300 raise. In the first six months you'd make $5,000, the second six months $5,300, the third six months $5,600, and so on. 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. Under that scenario Marilyn's right in saying you'd be $700 per year ahead after three years and $1,100 after five years. The difficulty here is that the question is ambiguous. So let's not blame Marilyn vos Savant, but rather the befuddled soul who wrote the original letter. It's a strategy that usually works for me.

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