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

Option 2 is the best: 2^0 = 1

Pay after 1 month (Assuming the month has 30 days):

2^29/100 = $5,368,709.12

$5,368,709.12 definitely beats $5000 for the first month.

Answer 2

Answer:

You pick the second option.

Your salary at the end of the first month will be $10,737,418.23

Step-by-step explanation:

Option 1:

$5000 for the next two months.

Option 2:

A geometric sequence, with common ratio r = 2.

The common ratio of a geometric sequence is the division of the term $a_{n+1}$ by the term $a_{n}$.

Here, the geometric sequence is {0.01, 0.02, 0.04,....}, since a penny is 1 cent.

The sum of the first n terms of a geometric sequence is given by the following formula:

$S_{n} = \frac{a_{1}*(1 - r^{n})}{1 - r}$

In which $a_{1}$ is the first term, so $a_{1} = 0.01$.

For the next two months, so 60 days.

$S_{60} = \frac{0.01*(1 - 2^{60})}{1 - 2} = 1.15 \times 10^{16}$

This is higher than $5,000, so you pick the second option.

How much will your salary be at the end of the first month?

$S_{30} = \frac{0.01*(1 - 2^{30})}{1 - 2} = 10,737,418.23$

Your salary at the end of the first month will be $10,737,418.23