# Percentage Calculation

October 19, 2012 4:15 PM Subscribe

I know the price of something now and what the price was 2 years ago - how do I calculate that as an annual percentage increase?

I live in Argentina where inflation is (unofficially) estimated at 25% annually. I remember that 2 years ago a kilo of ice cream at my local shop was 29 kilos. It's now 48 pesos. That's a 71% increase over 2 years - how do I calculate that on an annual basis (assuming the same increase each year)?

I've worked it out using trial and error, but I'm looking for a formula I can use and apply to other figures.

I live in Argentina where inflation is (unofficially) estimated at 25% annually. I remember that 2 years ago a kilo of ice cream at my local shop was 29 kilos. It's now 48 pesos. That's a 71% increase over 2 years - how do I calculate that on an annual basis (assuming the same increase each year)?

I've worked it out using trial and error, but I'm looking for a formula I can use and apply to other figures.

Usually you just take the 71% and divide it by the number of years, for your average annual increase. 35.5% annual increase.

I have no idea what the ^ means in JPD's formula.

posted by small_ruminant at 4:18 PM on October 19, 2012

I have no idea what the ^ means in JPD's formula.

posted by small_ruminant at 4:18 PM on October 19, 2012

Presuming you meant pesos not kilos, where'd you get 71%? It's 65.5%. So divided by 2 years is 32.75% average growth rate per year. But that doesn't mean it grew that much both years. If it grew that much both years, it would be 51.1 not 49.

posted by Dansaman at 4:22 PM on October 19, 2012

posted by Dansaman at 4:22 PM on October 19, 2012

It means exponentiation, because you need to do that.

If it increased 200% (tripled) after two years, your approach would say it increased by 100% (doubling) each year, but if that were true it would quadruple in two years instead of tripling.

Take the nth root of the the end price divided by the start price where n is the number of years.

√(48/29) = 1.29, a 29% increase.

posted by aubilenon at 4:23 PM on October 19, 2012

If it increased 200% (tripled) after two years, your approach would say it increased by 100% (doubling) each year, but if that were true it would quadruple in two years instead of tripling.

Take the nth root of the the end price divided by the start price where n is the number of years.

√(48/29) = 1.29, a 29% increase.

posted by aubilenon at 4:23 PM on October 19, 2012

small_ruminant's suggestion is incorrect. Percentage increases compound rather than add. As an example, $10 increased by 25% twice (ie, over two years), is $15.62, not $15.

JPD's suggestion is mostly correct (with the ^ being the exponent operator), where Pn is the "current" price, Pi is the "initial" price, and n is the number of years. However, it is really (Pn/Pi)^(1/n) to be complete. In this case, the result is (48/27)^(1/2), which is about 28.65% inflation.

posted by saeculorum at 4:24 PM on October 19, 2012 [1 favorite]

JPD's suggestion is mostly correct (with the ^ being the exponent operator), where Pn is the "current" price, Pi is the "initial" price, and n is the number of years. However, it is really (Pn/Pi)^(1/n) to be complete. In this case, the result is (48/27)^(1/2), which is about 28.65% inflation.

posted by saeculorum at 4:24 PM on October 19, 2012 [1 favorite]

small_ruminant's method unfortunately does not account for compounding.

posted by roomwithaview at 4:24 PM on October 19, 2012

posted by roomwithaview at 4:24 PM on October 19, 2012

Look up CAGR - compound annual growth rate on wikipedia for the formula

posted by Farce_First at 4:26 PM on October 19, 2012

posted by Farce_First at 4:26 PM on October 19, 2012

OK, so yes I meant pesos per kilo and yes, I meant 65% not 71%.

And it seems saeculorum and JPD have it - thanks all!

posted by jontyjago at 4:32 PM on October 19, 2012

And it seems saeculorum and JPD have it - thanks all!

posted by jontyjago at 4:32 PM on October 19, 2012

Yes, the technique I posted is the average arithmetic annual return, which is what most investments use for short term calculations, such as 2 years. Also, I think mutual funds use it no matter how many years, though I don't think they should be allowed to. C'est la vie.

Geometric is used for longer terms because it's more accurate over longer periods.

posted by small_ruminant at 4:49 PM on October 19, 2012

Geometric is used for longer terms because it's more accurate over longer periods.

posted by small_ruminant at 4:49 PM on October 19, 2012

mutual funds use compound growth rates for any annualized data longer than one year that complies to GIPS standards - which is considered best practice.

posted by JPD at 6:16 PM on October 19, 2012

posted by JPD at 6:16 PM on October 19, 2012

*Yes, the technique I posted is the average arithmetic annual return, which is what most investments use for short term calculations, such as 2 years*.

That's only because the smaller the % involved, the closer it approximates the correct formula. Financial calculations are always based on compound interest. JPD and saecularum's formula is the correct one.

posted by mr vino at 10:00 AM on October 20, 2012

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So here its Year2/Year0^(1/2)

posted by JPD at 4:17 PM on October 19, 2012