Property Tax Thoughts
The paper today reported Daniel’s property tax plan. "Daniels also wants the state to pick up the costs of schools' general funds, school transportation and child welfare and supports limiting local spending growth to the six-year average growth of personal income." Most people would think this sounds good. However, a mathematician would say it is not. The reason is simple and it comes down to the difference between an average and compound rate of change. The average of six years will always be higher than the compounded annual rate over that same six year period. In simple terms if they limit it to this, spending and ultimately taxes will grow far faster than our income.
Some will say, it is small, but in fact anything that is even slightly greater than the income growth of those being taxed will eventually become large. Why not just state it mathematically correct to begin with. It is not a difficult calculation. Anyone can perform it on a calculator.
The formula is:
Exp[ln(Fv/Pv)/# of years]-1 = compounded rate
Below are three examples. The first shows a small change, but the last to show a large difference. The reason is that a high first year will create a much larger difference.
The first column is the year, second column is a randomly generated rate of growth and the third column is the value of any given year.
0 $1.00
1 1.6% $1.02
2 5.5% $1.07
3 0.8% $1.08
4 5.7% $1.14
5 5.4% $1.20
6 1.8% $1.22
3.45% 3.42%
0 $1.00
1 9.9% $1.10
2 5.4% $1.16
3 1.3% $1.17
4 4.0% $1.22
5 4.9% $1.28
6 1.2% $1.29
4.44% 3.76%
0 $1.00
1 9.6% $1.10
2 3.9% $1.14
3 1.1% $1.15
4 7.6% $1.24
5 1.9% $1.26
6 7.7% $1.36
5.30% 4.48%
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posted by William Larsen @ 8:58 PM
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