What is the overall percentage increase

[TheCameraGeek]

So after going to arbitration, a union receives an award granting cost of living increases of 2% for the first year, 2.6% for the second year, and 1.4% for the final year of the contract. Most people I've spoken to say that that is an overall increase of 6%, but that doesn't make intuitive sense to me--I don't know if I'm using the right language, but there is compounding happening, boosting the overall rate a little bit. However, after making several attempts, I haven't been able to figure out what the actual increase is.

Any help would be greatly appreciated, thank you.

Keith

 

[Deleted member 4993]

So after going to arbitration, a union receives an award granting cost of living increases of 2% for the first year, 2.6% for the second year, and 1.4% for the final year of the contract. Most people I've spoken to say that that is an overall increase of 6%, but that doesn't make intuitive sense to me--I don't know if I'm using the right language, but there is compounding happening, boosting the overall rate a little bit. However, after making several attempts, I haven't been able to figure out what the actual increase is.

Any help would be greatly appreciated, thank you.

Keith

(1+x)(1+y)(1+z) = 1+ (x+y+z) + [xy + yz +zx + xyz] ≈ 1+ (x+y+z)

When x, y & z are small (say <0.01) you can neglect the terms in [], for approximation purposes.

 

[jonah2.0]

Way too hammered right now but I get the same impression as Sir Denis; that this might be a simple case of finding the level rate of interest i that would give the same accumulated value at the end of 3 years. Thus

(1.02)(1.026)(1.014)=(1+i)^3

By this interpretation, i is nowhere near the alleged overall increase of 6%.
This is of course just my beer soaked perspective. Tequila might just give me a different view in the next half hour. Or I might just be asleep by then.

Cheers.

 

[Deleted member 4993]

Way too hammered right now but I get the same impression as Sir Denis; that this might be a simple case of finding the level rate of interest i that would give the same accumulated value at the end of 3 years. Thus

(1.02)(1.026)(1.014)=(1+i)^3

i = 0.01998824 ≈ 2%

By this interpretation, i is nowhere near the alleged overall increase of 6%.
This is of course just my beer soaked perspective. Tequila might just give me a different view in the next half hour. Or I might just be asleep by then.

Cheers.

I think the alleged increase was 6% in 3 years (or 2% per year)

That matches with other interpretations.