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Question

Is a salary of 1 cent for the first half month, 2 cents for the second half month, 4 cents for the third half month 8 cents for the fourth half month, and so on until the year is used up, a good or poor total salary for the year? I think it is a good total salary for the year, but I am having a hard showing the work for this problem.

Answer 1

S = 1 + 2 + 2^2 + 2^3 + ... + 2^23

2S =0 + 2 + 2^2 + 2^3 + ... + 2^23 + 2^24

subtract:

S = 2^24 -1 = 16777215 which is in cents, so $167,772.15

Answer 2

month 1 = 1 cent
2 = 2 cents
3 = 4 cents
4 = 8 cents
5 = 16 cents
6 = 32 cents
7 = 64 cents
8 = 128 cents
9 = 256 cents
10 = 512 cents
11 = 1024 cents
12 = 2048 cents

The end of the year, the salary will be 2048 cents

From first month 1 cent to last month of the year 2048 cents. It is an increase of 2048%. So it is goog total salary for the year

Answer 3

It's an unbelievably good salary.

As it reads, you get paid every half month, so that's equal to getting paid every two weeks. First figure out how many times you get paid that year.

(12 months) x (twice per month) = 24 paydays

The first payday, you get 1 cent. The second payday, you get 2 cents. Third is 4 cents. Then 8 cents. This is implying that every payday, your salary will double. Now just do that 24 times.

1 - 0.01
2 - 0.02
3 - 0.04
4 - 0.08
5 - 0.16
6 - 0.32
7 - 0.64
8 - $1.28
9 - $2.56
10 - $5.12
11 - $10.24
12 - $20.48

Six months in, you're still only getting paid twenty bucks! But then ...

13 - $40.96
14 - $81.92
15 - $163.84
16 - $327.68
17 - $655.36
18 - $1,310.72
19 - $2,621.44
20 - $5,242.88
21 - $10,485.76
22 - $20,971.52
23 - $41,943.04
24 - $83,886.08

Your last paycheck at the end of the year will be $83,886.06, which is pretty darn good, and then for the total salary for the year, just add them all up and the grand total is $167,772.20. I don't know about you, but that a whole lot of money for me. I'd take that job.

Answer 4

The total salary is
1+2+4+8++...+2^23 = (2^23*2-1)(2-1)
sum of a geometric progression with r=2
S=$167,772.15

Answer 5

their is 24 half months in a year,so just add up 1-24 inclusive

Answer 6

Considering that $167772.15 is a good salary, Yes
Considering that $167772.15 is a poor salary, No
Please give me best answer thanks!

Answer 7

with a good old fashion calculator I got $167,772.15 after 23 pay periods and $335,544.31 after the 24th.