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Math pedant to the rescue! Actually, rates combine in a multiplicative way -- losing 3% and then 4% does not lose 7%, (though it's close). What if the economy
by clintonc 12y ago
Math pedant to the rescue! Actually, rates combine in a multiplicative way -- losing 3% and then 4% does not lose 7%, (though it's close). What if the economy lost 1% each day for a year? It would not lose 365%.
If we assume the annualized rate, the economy would be 97.1% of its current size in a year. The fourth root is 99.267%, so the economy shrank about 0.733% this quarter. If it does so for four consecutive quarters, it will decrease by 2.9%.
I know that's what you said in the first place, but when extrapolating further into the future, it makes a difference.
- sp332 12y agoActually I didn't think about annualized rates compounding like that, although it makes sense now that you mention it :)
- conistonwater 12y agoMath pedants of the world: If you calculate 1-(1-x)^(1/4), the difference between the true answer and x/4 is approximately 3 * x^2/32. For a figure of y percent, this is a relative error of 0.375 * y percent. Ignore it when y is small. The GDP figure is only known to something like 1 or 2 decimal places.
- deleted 12y ago[deleted]
- mtdewcmu 12y agoIf I'm not mistaken, if you keep following that thread, somehow or other you eventually get e. I hope that wasn't too much pedantry.