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GOOD PAY FOR GOOD WORK!
A Math Puzzle to Solve 


You've just been offered a job! The job is going to last for 30 days. You meet with your new employer to discuss the benefits, what the job is going to entail - you know.....all the specifics. Then comes the most important aspect of your job - the salary!

Your employer lays it all out for you. But it's not that simple, really. You have a decision to make, and you're not sure what to do. You'll have your choice of two payment options:

  • One cent on the first day, two cents on the second day, and double your salary every day thereafter for the thirty days;
------ or ------
  • Exactly $1,000,000. (Yes.....you heard it right.......That's one million dollars!)

Okay, now you're thinking........what's the catch? You know what the job is, you know that it's going to last for 30 days only. What's the best payment option? You're thinking, "I'll take the million! This is a no-brainer!" But wait! DO THE MATH! Which IS the best option? Make a chart to solve this dilemma.


SOLUTION

Direct students to complete a table similar to the one below to investigate the payment for the first week, using the first salary option:

First Option Payment - Week 1

Day No. Pay for that Day Total Pay (In Dollars)
1 .01 .01
2 .02 .03
3 .04 .07
4 .08 .15
5 .16 .31
6 .32 .63
7 .64 1.27


Oh, great! You have just completed one week of work, and all you have to show for it is a measley $1.27! That 1 million is looking pretty darn good right about now, isn't it? But, you're committed to seeing this thing through, just to prove to yourself that the second option of a million up front is your best choice. Check out the second week by filling out another table.

First Option Payment - Week 2
Day No. Pay for that Day Total Pay (In Dollars)
8 1.28 2.55
9 2.56 5.11
10 5.12 10.23
11 10.24 20.47
12 20.48 40.95
13 40.96 81.91
14 81.92 163.83


Okay, so this amount looks a little better, but you have to realize that you've worked for 2 weeks and you only have a little over $100.00. That million is definitely looking like the way to go! Let's see the third week.


First Option Payment - Week 3
Day No. Pay for that Day Total Pay (In Dollars)
15 163.84 327.67
16 327.68 655.35
17 655.36 1310.71
18 1310.72 2621.43
19 2621.44 5242.87
20 5242.88 10,485.75
21 10,485.76 20,971.51


Now we're cookin'! That's some serious coin! But, it's still not close to a million, and we don't have a whole lot of time left to make that money! So, the best deal here is to take the mill and run, right? Of course! And didn't we know that all along?! So, let's fill out the 4th week's chart just for the sake of finishing what we have started, okay?


First Option Payment - Week 4
Day No. Pay for that Day Total Pay (In Dollars)
22 20,971.51 41,943.03
23 41,943.04 83,886.07
24 83,866.08 167,772.15
25 167,772.16 335,544.31
26 335,544.32 671,088.63
27 671,088.64 1,342,177.27
28 1,342,177.28 2,684,354.55


Wait a minute! Look at that total! You have gone from $21,000.00 to over a million in 6 days! Check your work......this has GOT to be wrong! It's not? This is totally amazing! And you have two more days to work! I wonder what the final total will be? Let's see!


First Option Payment
Day No. Pay for that Day Total Pay (In Dollars)
29 2,684,354.56 5,368,709.11
30 5,368,709.12 10,737,418.23


Well, now! Looks like it's a good thing we stuck with the investigation! With the first option, in 30 days your pay increases from 1 penny to over 10 million dollars! I suppose you don't have to be a brain surgeon to figure out which option is your best choice. Congratulations!

 

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