# Trade union and employer make a two year collective agreement where they agree to increase the salaries as many percents both years. Eventually the increase was 5.5%. How many percents the salaries...

Trade union and employer make a two year collective agreement where they agree to increase the salaries as many percents both years. Eventually the increase was 5.5%. How many percents the salaries were increased per each year?

(I'm sorry for the poor translation, I'm not a native english speaker)

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This is an example of the time value of money. The first year it goes up a certain %. Then, the second year, it goes up another % on top of that. So, we would multiply the two together. We would have:

(1+x)^2 = (1+0.055)

x^2 + 2x + 1 = 1.055

x^2 + 2x - 0.055 = 0

So, solving the quadratic with the quadratic formula:

x = -2 +- sqrt(2^2 - 4*1*(-0.055))

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2*1

x = -2 +- sqrt (4 + 0.22)

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2

x = -2 +- sqrt(4.22)

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2

The subtraction would give a negative interest. That would drop out. So, only using the addition:

x = -2 + 2.0543

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2

x = 0. 02715

So, it went up 2.715% each year.