Here’s a good rule of thumb: if you’re trying to calculate how much money to send an insurance company, it’s probably a good idea to round up. That’s a lesson that La Rosa Carrington learned the hard way.
Carrington had health insurance under her job, and when she lost her job she was allowed to continue her health insurance under federal COBRA law. Trouble is, she didn’t get a bill so she estimated the amount she would have to pay: her payments were “a little over $471.87 per month” (according to The Gazette in Colorado Springs, where the story first appeared on July 6) but because of the 2009 American Recovery and Reinvestment Act she only had to pay 35% of that.
Carrington didn’t get a bill from Discovery Benefits, and yet she knew it was important to keep up the payments, especially because she was also undergoing chemotherapy for leukemia so details like current health insurance coverage were totally non trivial matters. She sent them a check for $165.15. Trouble is, Discovery Benefits said she owed $165.16, and canceled her coverage. She called, they refused to budge, and finally the supervisor did the calculation herself and decided that rounding the amount to $165.15 was actually right, or at least reasonable, and the penny was paid [either by the company or by a person in the company; it's not clear which].
So be warned: sending in that extra penny might be good insurance for your insurance.
The story could end there, since rounding is all mathematical in and of itself, but there’s a tangent that I’m still wondering about: what’s the deal with the monthly payments being “a little over” $471.87 each month? If the annual dues were $5662.46, for example, then the monthly payments would be $471.8716666…, which would round to $471.87, but 35% of the original $471.871666….. would actually be $165.155083333… which does round to $165.16 using conventional models of rounding. It seems plausible to me that the Benefits Computer was just rounding, and not necessarily rounding up all the time, and that the multiple rounds gave a difference of a penny, which would make this a story not about rounding up versus rounding down, but about the compounding of rounding errors. I looked at a few different reports on this, though, and never saw mention of this so it’s possible that the Benefits Computer was automatically rounding up for all rounding as implied.