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I am trying to calculate the cumulative salary increase across 10 years. The issue is that some union members received raises multiple times a year, and other years they received no raises. I am struggling to figure out a formula that can compound their total wage increase across the 10 year period.

The data I have is as follows (example):

2007 - Apr 10 - 3.2% increase
2007 - July 05 - 0.9% increase
2008 - April 01 - 2% increase
2008 - May 28 - 0.5% increase
2008 - June 30 - 1% increase
2009 - 0% increase
2010 - 0% increase
2011 - 0% increase
2012 - Sept - 2.5% increase
2012 - October - 0.5% increase
2013 - October - 1% increase
2014 - 0% increase
2015 - July - 1% increase
2016 - July - 1.5% increase
2017 - Sept - 0.1% increase

I would appreciate any support in pushing me in the right direction.

Thank you!

  • 2
    It doesn't matter when it was, a 1% increase followed by another 1% increase is still a 2.01% increase. – Kevin Sep 11 '17 at 20:44
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The TOTAL increase is just be the product of all increases (in (1+r) terms):

1 + r_total = 1.032 * 1.009 * 1.02 * 1.0005 * ...

The time frame of each raise is not relevant since you're wanting the total increase.

By my calculations, the total product is 1.151, or a total increase of 15.1%.

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If you want to calculate the annualized increase from D Stanley's total, you would simply take the 10th root of 1.151 which leaves you with 1.01416 or an average yearly increase of 1.42%.

A simpler formula would be to take the final rate, divided by the initial rate (that would give you the cumulative total) then take the 10th root of that total for the annualized increase.

If the union was being paid $10/hr in 2007 and $11.51/hr in 2017, you could see that rate as follows:

(11.51/10)^1/10 = 1.01416...

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