Inflation calculation help

atypical

I’m trying to calculate the value of something in Jan 2007 compared to Jan 2012. The CPI tables here show that the CPI index was 103.2 in Jan 2007 and was 121.1 in Jan 2012.

So to calculate what £1,000 in Jan 2007 needs to have increased to in Jan 2012 to have kept its value I do the following:

Cost in Jan 2007 x (2012 price index / 2007 price index) = Cost in Jan 2012

£1,000 x (121.1 / 103.2) = £1,173.45 or 17.35% increase (+ £173.45).

If I want to calculate what £1,000 in Jan 2007 has decreased to in Jan 2012 I do the following:

Cost in Jan 2007 x (2007 price index / 2012 price index) = Cost in Jan 2012

£1,000 x (103.2 / 121.1) = £852.19 or 14.78% decrease (- £147.81)

But shouldn’t the increase and decrease be the same? This makes me think I’m doing something wrong. I know the first calculation is right. But how do I calculate what £1,000 in Jan 2007 has decreased to in Jan 2012?

Thanks a lot for any help.

Stompa

Your calculations are correct, the percentage increase and decrease shouldn't be the same. After all, if you reduce 100 by 20% you get 80, to get back to 100 you have to increase 80 by 25%.

Lokolo

You are correct I think. If you do £852.19 * 1.1735 (so 17.35% increase like in your first calculation) you arrive at £1k.

I can't explain it, but it's the same as income tax.

If you want to find out how much tax you owe, you take off 20%. But if you want to go the other way around (so find out your gross if you have net) you have to add 25%.

Sceptic001

Put another way, there is a limit of 100% when considering a decrease. A price cannot go below zero. But the scope for an increase is infinite.

So you could reasonably argue that a 50% fall is more significant than a 50% rise. No wonder politicians can obfuscate so easily with statistics.

atypical

Which is the correct percentage to use? Has the value of the £1,000 decreased by 17.35% or 14.78%?

talexuser

Depnds on where you start. The whole point is the £1000 is not £1000 in absolute terms at both dates. The newer £1000 is worth less than the older £1000 (ie approx £852) and that is why the 2 percentages in the different directions are not the same, you're starting from different absolute values and a percentage is just a fraction of the starting value.

atypical

I suppose the better question to ask then is which would be the more appropriate figure to use? Is it more conventional to use the first (17.35%)?

And if I use 17.35%, is it right for me to say that that is the equivalent of a 3.25% annual decrease in value?

Stompa

atypical wrote: »

I suppose the better question to ask then is which would be the more appropriate figure to use? Is it more conventional to use the first (17.35%)?

And if I use 17.35%, is it right for me to say that that is the equivalent of a 3.25% annual decrease in value?

If it was worth £1000 in 2007 and £852.19 in 2012, then you'd say the value has decreased by 14.78%. Which would be equivalent to an annual decrease in value of 2.76%, since

1.0276 x 1.0276 x 1.0276 x 1.0276 x 1.0276 = 1.1478 (roughly)

pqrdef

atypical wrote: »

I suppose the better question to ask then is which would be the more appropriate figure to use?

Depends what you want to say. The pound has decreased in value by 14.78% since 2007.

But equally, it was worth 17.35% more in 2007 than it is now.

The construction of the statement implies what you're taking as the base. In the first statement, the 2007 value, and in the second statement, the current value.

King_Weasel

Just to muddy the waters, you could question whether you want to use a bogus index like the CPI or the proper one, the RPI.

atypical

pqrdef wrote: »

Depends what you want to say. The pound has decreased in value by 14.78% since 2007.

But equally, it was worth 17.35% more in 2007 than it is now.

The construction of the statement implies what you're taking as the base. In the first statement, the 2007 value, and in the second statement, the current value.

Thanks, I think I finally understand it now.