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Tuesday, March 22, 2011

$10mil or penny doubled 30 days- Which is more?

When I was younger, to demonstrate value of money and lack of understanding most have about it, I was posed a situation--  I took a job for 31 days and the boss offered me two choices how I would be paid.  First choice is to take a lump sum payment of $10 million dollars after 31 days.  The second choice is to accept 1 penny for the first day of work, but the salary would continuously double each subsequent day and I would get paid the total amount at the end of the work period  (2 cents paid on day 2;  4 cents paid on day 3, etc)?

Most people would take the $10 million.  After all, it averages $333k/day.

But would that be the most financially sound choice?

Here's a day by day breakdown of wages doubled daily starting at a penny:

Day  1 -    0.01       a penny
Day  2 -    0.02       3 cents total
Day  3 -    0.04       7 cents earned in 3 days
Day  4 -    0.08       15 cents total
Day  5 -    0.16       31 cents earned after 5 days
Day  6 -    0.32       63 cents total
Day  7 -    0.64       $1.27 earned after 1 full week

~  Looks pretty bad- $10mill looks good..  Let's resume..

Day   8 -    1.28        $2.55 total
Day   9 -    2.56        $5.11 total
Day 10 -    5.12        $10.23 earned after 10 days
Day 11 -  10.24        $20.47 total
Day 12 -  20.48        $40.95 total
Day 13 -  40.96        $81.91 total
Day 14 -  81.92        $163.83 earned after 2 full weeks

~  That's better than after 1 week but nowhere near $10mill, hmm...

Day 15 -    163.84     $327.67 total  (halfway there)
Day 16 -    327.68     $655.35 total
Day 17 -    655.36     $1310.71 earned in 17 days
Day 18 -  1310.72     $2621.43 total
Day 19 -  2621.44     $5242.87 total
Day 20 -  5242.88     $10,485.75  total
Day 21 - 10,485.76   $20,971.51 earned in 21 days

~ This isn't looking too good.. gulp~  10 days to go

Day 22 -      20,971.52           $41,943.03  total
Day 23 -      41,943.04           $83,886.07  total
Day 24 -      83,886.08          $167,772.15 earned in 24 days
Day 25 -    167,772.16          $335,544.31 total
Day 26 -    335,544.32          $671,088.63 total
Day 27 -    671,088.64         $1,342,177.27 total
Day 28 -    1,342,177.28      $2,684,354.55 earned in 28 days

~  3 work days left.. looks promising...

Day 29 -   2,684,354.56       $5,368,709.11  total
Day 30 -   5,368,709.12     $10,737,418.23  total  (1 day left)
Day 31 -  10,737,418.24    $21,474,836.47

A penny, doubled each day for 31 days =  $21,474,836.47

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