For comparison, our school's fees have increased each year since September 2012 as follows: 7%, 6%, 3.7% and just announced 3.5% from next September. This makes an overall increase of 21.8% over four years.
Percentages don't quite work like that:
Take £100 and increase it by 10% - that's £110
Now increase again by 10% - that's £110 + £11 = £121
So compared to £100 we have a 21% increase not a 20% increase ...
I didn't say our school's fees increased by 20%, it was 21.8%.
I only mentioned the 20% as a ceiling some schools don't seem to have exceeded and that perhaps has muddled things up a bit.
The 21.8% increase was calculated by dividing next September''s fees by 2012 fees, not by compounding individual annual increase rates. There is a slight discrepancy due to rounding, i.e. I quoted percentages rounded to either a whole number or one decimal point.
If I were to compound percentage changes shown to two decimal points, it would be as follows:
Year 1 increase: 6.96%
Year 2 increase: 6.02%
Year 3 increase: 3.74%
Year 4 increase: 3.50%
Compounded increase: 21.76%
I calculate this by going 1.0696 x 1.0602 x 1.0374 x 1.0350 = 1.2176.
1.2176 - 1 = 0.2176 = 21.76%
Is there a different way of doing it?