Nice, that is a lot of math. 
Oh, you're right, I was quoting quick speed interest rate because I'm so used to quick speed. I'm not sure if I understand what you're saying directly after that, though. IMO the normal speed interest rate is going to be correspondingly lower (so that the doubling time is about +50% compared to quick), but the compounding time will not be increased so much due to the higher time resolution (therefore leading to a slightly more efficient economy on normal speed). (For example, on both quick and normal speed, it takes a minimum of 2 turns to start and then whip a settler.)
Regarding the mean compounding time, slavery has a big impact on it (and it's a major reason that slavery is good). My unresearched estimate would be that on quick it's 5 turns, and on normal it's 7.
Quote:Let's work normal speed, and take it as given that 1=2 in 30T. This is an estimate of the mean interest rate. Please note that if investments compound per turn, then the normal speed interest rate is not 3.53% as in quick speed. Instead it is 2^(1/30)=2.38% which I think foreshadows the importance of a mean compounding time >1. I suspect that the mean interest rate is the same or similar when comparing quick and normal speed. It is the mean compounding time that scales between the two settings and gives 1=2 in 20T (quick) <=> 1=2 in 30T (normal).
Oh, you're right, I was quoting quick speed interest rate because I'm so used to quick speed. I'm not sure if I understand what you're saying directly after that, though. IMO the normal speed interest rate is going to be correspondingly lower (so that the doubling time is about +50% compared to quick), but the compounding time will not be increased so much due to the higher time resolution (therefore leading to a slightly more efficient economy on normal speed). (For example, on both quick and normal speed, it takes a minimum of 2 turns to start and then whip a settler.)
Regarding the mean compounding time, slavery has a big impact on it (and it's a major reason that slavery is good). My unresearched estimate would be that on quick it's 5 turns, and on normal it's 7.