Story problem I can not figure out

Question

math help: would you rather sign an open ended contract that compensates you with a one time only 15,000 signing bonus plus $200 for each day you work OR be paid $1 if you work 1 day, $2 if you work two days, $4 if you work 3 days, $8 if you work 4 days, and so on?

Answer 1

Unless you expect the project to be extremely short, the 2nd terms are astronomically better. The break even point after x days is when 15000+200x ≤ ∑2^x-1

Say the project lasted at least 15 days. Under the first terms, you would have received 18,000 in total. Under the 2nd terms, you would receive 32,768 on that day alone.

Answer 2

Great answer, Larry C!!! Yes, I agree with Larry that the 2nd terms are better if the job is long-term, however, if expected to be less than 2 weeks, the first option is what you should choose!! If this was a real scenario, congratulations would be in order for having such great compensation choices!