Originally Posted by

**billy ross**
In both of your examples you are describing deviation from trend or from average. However, we're talking financials here, year over year performance, where each year builds upon the previous year, and changes in financial numbers are generally measured per cent per annum. Thus stock market returns and interest rates would generally be described per cent per annum. Sometimes a cumulative return over a longer period is used, as I earlier used a 45% increase over 10 years in property values in Philly, but that tends to confuse things since everything else is measured per annum and not per decade. The fact that we're talking about a stretch which lasts at least two years here means that changes need to be adjusted to account for how many years they are averaged over. In this case it is at least two years, but it may be longer. If I pay 7% per annum to the bank for money I borrow and it goes on for two years, I'll have owed them 14%. However, most people would still consider that I paid 7% per annum. Similarly, if I only borrowed the money for one month, the interest may be calculated on a per diem basis, but it is generally expressed and understood on a per annum basis.

Fundamentally in every period the base changes due to what happened in the previous period, and the change during that period is calculated relative to the baseline at the beginning of the period. To calculate things relative to day one all of the time would be quite confusing. I think the reason you're confused is that you for whatever reason refuse to use compounding. Any successful investor knows and appreciates the value of compounding your return. To use real numbers, the real increases are less than 10 and 4. In reality, they're 9.9% and 3.8%, I believe. Despite the fact that they're less than the numbers that you use, the front-end loading of the tax increase combined with the effect of compounding causes the tax in year two to be $114.08, which is less than 7% per annum. Do you calculate your annual salary increases based upon what your salary was when you first joined the company, or do you calculate them based upon what it was immediately before the latest increase? If you started out at $10 per hour and after much hard work you get a raise from $20 per hour to $22 per hour, you got a 10% raise, not a 20% raise.

There are places I own where the rents are twice what they were when I first bought the place. I have a place coming up now where the rent was $700 per month when I first renovated it. Now the rent is $1,300 per month. There is great interest in the house at $1,400 per month. While the rents will have doubled (if I get a taker at that number) since I first renovated it back in 1999, I only count it as a $100 rent increase, since my baseline rent now is $1,300 per month. I have another place where I granted a concessionary rent of $400 per month temporarily before I put someone else in at $550 (I believe) back in 1998. Now the rent is $800, and it has been for over two years. If I rent it at $850 or $875, I'll count it as an increase of $50 per month or $75 per month, not $450 or $475 per month. I think the problem is that you're not changing your baseline for year two, and that's why you see it as a whacky 12% average increase. You're averaging two years increase over the baseline in the very first year, which of course wasn't even the very first year, since Philly has been collecting property taxes for centuries. I'd love to see a regression comparing the property taxes in Philly versus property values in Philly over time, and to know how that compares to our suburbs and other cities. My suspicion is that it would show that in Philly property taxes have been trending cheaper, both relative to our historical performance and relative to our competitors. I'm not sure, though. This recent 14% jolt has been an attempt to rectify that, and I hope that it trends back to the mean.

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