Question

If your employer asked you to select one of these options:
Option 1: Your salary for the next two months will be $5,000.
Option 2: 1 penny for the first day; then, he will double your salary every day for the next two months.
Which would you pick and how much will your salary be at the end of the first month?

Answer 1

Well idk option 2 but option 1 should be $2,500 for the first month

Answer 2

It would depend on the number of days in the month but the sequence is a geometric one.  And it grows very rapidly so I'd pick that, and the sum can be expressed as:

s(n)=a(1-r^n)/(1-r)  here a=0.01 (a cent) and r=2 so

s(n)=0.01(1-2^n)/(1-2)

s(n)=-0.01(1-2^n)  so just assume a 28 day month, in the first month you will earn

s(28)=-0.01(1-2^28)=$2,684,354.55  Yes that is over two and a half million dollars in the first month :P

On that 28th day you will earn:

a(28)=0.01(2^(28-1))=$1,342,177.28