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In one excel workbook I am working on right now, the annual mortality rate is given as 3.082%

And the formula for calculating the daily mortality rate is 1-EXP(LN(1-[annual mortality rate]/365)

Why is it not 3.082%/365? What are the e^() and natural logs implying about the assumptions we're making converting from annual to daily rate?

Thank you.

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  • $\begingroup$ You should ask here - math.stackexchange.com . I'm not sure about what exactly you mean by rate, but notice that $(1-AR) \neq (1- \frac{AR}{365})^{365} $ $\endgroup$
    – meh
    Commented Jul 8, 2017 at 4:08
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    $\begingroup$ I suspect you haven't quoted the formula correctly; the parentheses are misplaced. The correct one is $$1-(1-0.03082)^{1/365} = 1-\exp\left(\frac{1}{365}\log\left(1-0.03082\right)\right)\\=0.0000857632 \approx 0.0000844384 = \frac{0.03082}{365}.$$ $\endgroup$
    – whuber ♦
    Commented Jul 20, 2017 at 22:33
  • $\begingroup$ Thanks for this answer! I double checked the parentheses... they seem to be what I wrote above? Maybe the original person who made the workbook didn't do it right? As for rate, I mean mortality rate. @whuber If the result from our formula is similar to the 0.03082/365, do you have a guess as to why the original person (who I can't contact anymore) used a more complicated formula (as opposed to plain old [annual mortality rate]/365)? $\endgroup$
    – Aywfto
    Commented Jul 22, 2017 at 18:22
  • $\begingroup$ Your expression will not work, Christina, because the parentheses are unbalanced. One doesn't need to guess about the reason for the formula: this is a standard one for calculating with compound interest. $\endgroup$
    – whuber ♦
    Commented Jul 22, 2017 at 20:02
  • $\begingroup$ Ahh! i see. You're right -- it looks like its 1-EXP(LN(1-[annual mortality rate])/365) ^is that the standard one for calculating with compound interest? That makes sense then! $\endgroup$
    – Aywfto
    Commented Jul 24, 2017 at 18:15

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This seems to be a strange way to give the same result as you suggest. EXP(LN(X))=X. In this case X=1-(annual mortality rate/365) and therefore 1-X=annual mortality rate/365!

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  • $\begingroup$ Of course you're correct; but please see my comment to the question for a more constructive interpretation. $\endgroup$
    – whuber ♦
    Commented Jul 20, 2017 at 22:35
  • $\begingroup$ You are being a little more explicit but annual mortality rate/365 is in this case obviously 0.03082/365. $\endgroup$
    – Michael R. Chernick
    Commented Jul 20, 2017 at 22:58
  • $\begingroup$ That's not so obvious to me--indeed, your have just re-asserted the question. $\endgroup$
    – whuber ♦
    Commented Jul 21, 2017 at 13:22

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