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I don't frequent this board as often as I probably should and I just noticed a rather grievous error on my part... Thanks to JABoa for pointing it out. I often post from work and remember whipping off the post that contained the error... even though I was in a hurry I should have been able to eyeball that and know something was fishy about it... bad juju on my part. Nothing is worse than half the truth... and of course there is more than one sin here but the others are between me and my boss... ;-) (although they know I do this posting stuff at work and don't seem to mind... my mom would probably spank me if she knew though... ;-))

JABoa's correction is below

While LLNunn's explanation that more rapid compounding increases the APR is the right idea, there has to be something else going on here. There is a limit to the rate that more rapid compounding will reach, and 9.9% is too high.

For those who care, the amount owed on a balance of 1 at a rate x for n periods is (1 + x/n)^n, and if we fix x and increase n (the idea being that the interval between compounding periods decreases as n increases, so that the total time is the same), then in the limit of arbitrarily large n, we get exp(x).

If you took calculus you were taught this.

So with x = .069, exp(x) = 1.0714, i.e. 7.14% in the limit of continuous compounding. So something else is going on but I don't know what it is.
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