Saka-kun's Projects

The other day I had myself a customer that asked me this question:  "Can you save a penny a day for a month?"  Of course my response was yes.  In return with a grin on his face, "Could you still save a penny a day but every day double the amount you saved the previous day?"  Just for those may get the wrong idea, $0.01 first day, $0.02 the second, $0.04 the third and so on.  Before I could respond he said, "I bet you can't!"

So after a rather legthy discussion with the man and a calculator he was right.  Thankfully I'm not a betting person.  I have put few examples of this below, just show you the math of it all.  The only thing I was able to say to this was, "WOW".

Example One – Saving a penny a day.

Example Two – Saving a penny a day and doubling the amount to save every day.

Example Three – Saving a penny a day and doubling the amount saved every day on top of what is saved so far.

Day Example 1 Example 2 Example 3
1 $0.01 $0.01 $0.01
2 $0.01 $0.02 $0.03
3 $0.01 $0.04 $0.09
4 $0.01 $0.08 $0.27
5 $0.01 $0.16 $0.81
6 $0.01 $0.32 $2.43
7 $0.01 $0.64 $7.29
8 $0.01 $1.28 $21.87
9 $0.01 $2.56 $65.61
10 $0.01 $5.12 $196.83
11 $0.01 $10.24 $590.49
12 $0.01 $20.48 $1,771.47
13 $0.01 $40.96 $5,314.41
14 $0.01 $81.92 $15,943.23
15 $0.01 $163.84 $47,829.69
16 $0.01 $327.68 $143,489.07
17 $0.01 $655.36 $430,467.21
18 $0.01 $1,310.72 $1,291,401.63
19 $0.01 $2,621.44 $3,874,204.89
20 $0.01 $5,242.88 $11,622,614.67
21 $0.01 $10,485.76 $34,867,844.01
22 $0.01 $20,971.52 $104,603,532.03
23 $0.01 $41,943.04 $313,810,596.09
24 $0.01 $83,886.08 $941,431,788.27
25 $0.01 $167,772.16 $2,824,295,364.81
26 $0.01 $335,544.32 $8,472,886,094.43
27 $0.01 $671,088.64 $25,418,658,283.29
28 $0.01 $1,342,177.28 $76,255,974,849.87
29 $0.01 $2,684,354.56 $228,767,924,549.61
30 $0.01 $5,368,709.12 $686,303,773,648.83
31 $0.01 $10,737,418.24 $2,058,911,320,946.49
Total $0.31 $21,474,836.47 $3,088,366,981,419.73