In theory it's 1/4 not half. If you use ALL your points within 60 days window they are at half points. You double your points which means your maintenance fee costs are spread across twice as many points you own. It's simple math.
So at the end of the day, the math has to add up 55plus - can we agree on that? So, the math specific to the MF rates, has to actually add up to what the VIP owner actually pays for their MFs on the actual number of points that they own on an annualized basis - otherwise all of the "theory" doesn't matter when it comes to the "funny money" math with respect to effective MF rates.
So let's use your own numbers as an example. Let' say that MF rate is $6.00/1000 as we have been saying all along. Let's assume this VIPP owner has exactly 1MM points. This means the VIPP owner is paying exactly $6000/year for his MFs on his 1MM points. Agreed?
Now let's use your assumptions and assume for a moment that the VIPP books every single transaction within the 60 day window. So if we double the effective points to 2MM, and cut the MF rate in half:
2MM * $3.00/1000 = $6000.00
So you are correct in your overall assumption. But, your math was wrong for the individual example, because in your actual equation - you didn't double the number of points you divided in in half, as someone else already pointed out:
It is incorrect because you are applying the 50% discount twice at the same time.
The reservation may be calculated either (100,000 points x 50%) x $6/point =$300 for the reservation OR 100,000 points x ($6/point x 50%) = $300 for the reservations.
Do you see how the 50% discount is correctly applied only once in each of the calculations?
You are saying:
My bad, it should be $3 x 500 points = $150. Half points at half the cost of maintenance fees.
Big picture. Forget free or costs for guest certificates. Forget commissions or PayPal fees. Forget free upgrades even though that has value. Bottom line: 100000 points x $6 = $600 v. 50000 points x $3 = $150. This is fact, not theory. $150 is 1/4 of $600. How is this incorrect?
So how are you incorrect? The proof is in the pudding yes? So let's use your math to actually reverse engineer what the actual VIP owner would be paying per year in MFs, which has to add up at the end of the day:
100000 points x $6 = $600.00
Assuming 1MM points: $600.00 x 10 (source: 100000 x 10=1MM real points total) = $6000.00 - matches up to what the VIP owner actually pays
VERDICT: VALID/CORRECT
50000 points x $3 = $150.00
Assuming 2MM points: $150.00 x 20 (source: 50000 x 20= 2MM effective points total) = $3000.00 - does NOT match up to what the VIP owner actually pays
VERDICT: INVALID/INCORRECT
So, according to your own math/assumptions, the MF rate MUST be a constant in order to add up to the REAL amount of MFs that the VIP owner pays:
50000 points x $6 = $300.00
Assuming 2MM points: $300.00 x 20 (source: 50000 x 20 = 2MM effective points total) = $6000.00 - matches up to what the VIP owner actually pays
VERDICT: VALID/CORRECT
Hopefully this shows you where your assumptions/equations are incorrect. Bottom line is if you play out your numbers and they do not add up to
what the MFs are that are actually paid out, then your assumptions/equations are not valid.