How to figure compungd savings over a time period.

Question

A group of workers have a 5 year contract. If the workers agree to take no pay raise in a specific year of the overall contract how do I figure how much money that saves the employer over a specific time period. For example there are 10 workers who each make $50,000 a year. They have a contract that states they will receive a 2.5% raise every year for 5 years. If that take no raise in year 2 what is the savings to the employer over a ten and twenty year period.

Answer 1

I use a geometric sequence:

a_n = 50000(1.025)^n-1

For one worker getting the raise

S₁₀ = 50000((1 - (1.025¹⁰)) / (1 - 1.025)

S₁₀ = 50000(1 - 1.28) / -0.025

S₁₀ = 50000(-0.28) / -0.025

S₁₀ = -2000000(-0.28)

S₁₀ = 560000

 

With the raise one man earns $560,000 in ten years. Without the raise one man earns $500,000 -  $60,000 less.

For the ten men the savings is $600,000.