Problema Solution
Bill Gates offers you a job for one month. He gives you a choice of one of the two possible salary schemes: you can receive either a sum of $10,000 a day for each day of the month (including weekends), or you will receive your payment according to the following formula: 1 cent for the first day, 2 cents for the second day, 4 cents for the third day, 8 cents for the fourth day etc. Which payment would you choose and why?
Answer provided by our tutors
Let us check which of the two possible ways gets us more money.
Let us take a month of 30 days.
By first possiblity our salary would be= number of days * 10,000
= 30*10000 = $300000
In the second case the amount earned in 30 days = $(0.01+0.01*2+0.01*2^2 + 0.01*2^3+...+0.01*2^29)
This is a geometric series sum with first term, a = 0.01
and the ratio, r = 2
Sum of a geometric series is given as = a*(r^n-1)/(r-1)
= 0.01*(2^30-1)/(2-1)
= 0.01*1073741824
=10737418.24
Total salary in the second case = $10737418.24
This is more than the salary in the first possibility. He should choose the second possibility for the salary.