As Prize-money,
In the first deal, You will be given $ 5 million all at once.
In the Second Deal, you will be given one penny & double it each day for a month. (first day : 1 penny; 2nd day: 2 pennies; 3rd day :4 pennies, 4th day: 8 pennies. So on & so forth for 30 days)
How much money you can get in each of the deals?
Show your computational skill & come up with the BEST answer.
2006-08-21 07:12:36 · 12 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
I'd go with the second one $10,737,418.23
Day1 = 0.01
Day2 = 0.02
Day3 = 0.04
Day4 = 0.08
Day5 = 0.16
Day6 = 0.32
Day7 = 0.64
Day8 = 1.28
Day9 = 2.56
Day10 = 5.12
Day11 = 10.24
Day12 = 20.48
Day13 = 40.96
Day14 = 81.92
Day15 = 163.84
Day16 = 327.68
Day17 = 655.36
Day18 = 1310.72
Day19 = 2621.44
Day20 = 5242.88
Day21 = 10485.76
Day22 = 20971.52
Day23 = 41943.04
Day24 = 83886.08
Day25 = 167772.16
Day26 = 335544.32
Day27 = 671088.64
Day28 = 1342177.28
Day29 = 2684354.56
Day30 = 5368709.12
Sum = 10737418.23
2006-08-21 07:22:12 · answer #1 · answered by thatgirl 6 · 1⤊ 0⤋
In the second deal, you will get approximately $10 million.
On day x, you will get 2^(x-1) pennies. For example, on day 1, you get 2^0, or 1 penny. On day 2, you get 2^1, or two pennies. On day 30, you get 2^29 pennies. For any given day, the total number of pennies you got on all the previous days added together equals one less than the number of pennies you get on that day. For example, on day 4, you get 8 pennies. Over days 1, 2, and 3, you got 1+2+4, or 7 pennies. On day 6, you get 32 pennies, Over days 1-5, you get 1+2+4+8+16, or 31 pennies. So, over all the days before day 30 (when you get 2^29 pennies), you got 2^29-1 pennies. So the total number of pennies you get during the month is 2*2^29-1, or 2^30-1, pennies. That's 1,073,741,824 pennies, worth approximately $10 million.
So, on the surface, it looks like option 2 is the better deal. But if you take option 2, you have to wait a month before you get your full prize, and you get it all in pennies. I don't know about you, but I'd rather save all the hassle and just take the $5 million in crisp 20's
2006-08-21 07:29:18 · answer #2 · answered by knivetsil 2 · 0⤊ 1⤋
I WILL OPT FOR THE SECOND DEAL(30 days)
The first deal you get $5 million flat
The second deal.......after doubling the pennies for 30 days you get 536,870,912 pennies. Everyone knows there are 100 pennies in a dollar,therefore you get 36,870,912 pennies more than $5 million dollars.Therefore in the second deal you make $368,709.12 more than the first deal.
2006-08-21 08:10:57 · answer #3 · answered by princess 4 · 0⤊ 1⤋
The second deal is an exponential function modelled by:
y = 2^x
and day 1 is x = 0
Where y represents total value of pennies.
After the 30th day, you get 1.07 * 10^9
Hence, a billion pennies, or 10 million dollars.
I'd still choose to get 5million lump sum because after investing in stocks, I'd have 15million by the end of a month anyways :D.
2006-08-21 07:36:51 · answer #4 · answered by Krzysztof_98 2 · 0⤊ 1⤋
5th: 16,
6th: 32,
7th: 64,
8th: 128,
9th: 256,
10th: 612,
11th: 1224,
12th: 2448,
13th: 4896,
14th: 9792,
15th: 19584
16th: 39168
17th: 78336
18th: 156672
19th: 313344
20th: 626688
21th: 1253376
22th: 2506752
23th: 5013504
24th: 10027008
25th: 20054016
26th: 40108032
27th: 80216064
28th: 160432128
29th: 320864256
30th: 641728512
That would equal to: $6,417,285.12 for just the last DAY!
That is more than the 5 million so I would take the pennies.
2006-08-21 07:27:23 · answer #5 · answered by Anonymous · 0⤊ 1⤋
I'd take the second deal because on the last day of the month you'd get $5,368,709.12. Plus all the rest you end up with close to 10 million dollars.
2006-08-21 07:32:34 · answer #6 · answered by Mann 2 · 0⤊ 1⤋
With the second option, you'd have about $20 million after a month.
2006-08-21 07:21:51 · answer #7 · answered by DavidK93 7 · 1⤊ 0⤋
Deal # 2 is better cuz you end up with more $$$ than you can shake a stick at. 5 mil is only a fraction.
2006-08-21 07:19:52 · answer #8 · answered by dandelionsoup 3 · 1⤊ 0⤋
Deal number 2 is better.
In deal one, you get $5M
In deal two, you get $(2^30)=$1.07B/100 because it is geometric series.
in other words, $5,000,000 vs. $10,700,000. See the difference?
10 million is twice as large as 5 million
2006-08-21 07:37:38 · answer #9 · answered by gtn 3 · 0⤊ 1⤋
Definitely the second... it doesnt appear to be the best option, but it truly is.
2006-08-21 08:44:30 · answer #10 · answered by Jessica 2 · 1⤊ 0⤋