Which option would you choose , and why ?

Question

A . One penny the first day , two pennies the second day , four pennies the third day , and so on for 30 days .
B . $100 a day for 30 days .

Please tell me the answer and why . [Show Work]
I'm still trying to figure out how to give points .. If I find out , I'll give em to the best answer..er. [:

Yeah , Option A is obvious but teacher makes me show work . :P

>_>

Answer 1

I would take option a because, it has more money
According to your calculation the total amount in 30 days in option A has 536870912, total money is 1073741824 wheras in option B it's only 3000$

Answer 2

Without a second of thinking option A. Haven't u heard or read about the power of compounding? Even Einstein said that it is the eighth wonder of the world.

From option A we will get :

Day 1 = 1 penny (2^0)

Day 2 = 2 pennies (2^1)

Day 3 = 4 pennies (2^2)

Day 4 = 8 pennies (2^3)
and so on.....
hence after n days we will get 2^(n-1) pennies

Therefore after 30 days we will get 2^29 pennies that is 536870912 pennies. That is $ 5368709.12 or $ 5.3 million.

Option B

$100 per day for 30 days

$100 x 30 = $3,000

I'm sure everyone can figure out that $5.3 million is a hell lot more than $3000. So start believing in the power in compounding. Good Luck.

Answer 3

Option A

the process is about doubling each day

day 1 = 1 penny (2^0)

day 2 = 2 pennies (2^1)

day 3 = 4 pennies (2^2)

day 4 = 8 pennies (2^3)

etc....

so after n days you will get 2^(n-1) pennies

so after 30 days you will get 2^29 pennies (and i will leave you to convert into dollars for yourself but it promises to be HUGE)

Option B

$100 per day for 30 days

$100 x 30 = $3,000

so would yeild less than option A in the time allotted

PS if you follow the right buttons it will lead you into choosing a best answer for yourself and the 10 points will be automatically awarded upon your decision as are the two points awarding for anyone who answers this question

hope all that helps

Answer 4

A.
1 + 2 + 4 + 8 + 16 + .....
Since
1 = 2^0
2 = 2^1
4 = 2^2
8 = 2^3
etc.
we can see that on the 30th day you will get 2^29 pennies. That's more than a million pennies! (or more than 10,000 dollars.)

From this we know that if we choose A. we will get more than $10,000.

B.
$100 a day for 30 days is simply $3,000.

------
We notice that the total amt. you will get from B is less than the amt. you get on the 30th day of choice A alone.

So to get more money choose A.

^_^

Answer 5

I would choose option A. Here is why...

According to option A, starting from 1 penny on day 1, the amount is doubled everyday thereafter..
So, in 30 days, total amount earned would be:
1+2+4+8+16+32+64+128+256+512+1024+2048+4096+8192+16384+32768+65536+131072+262144+524288+1048576+2097152+4194304+8388608+16777216+33554432+67108864+134217728+268435456+536870912.

And the sum above = 1073741823pennies
or 10737418.23 dollars.

And option B says $100 for 30 days = $3000 in total..

Answer 6

Option A: after 30 days, you will make:
1+2+4+8+.....for 30 days. This is a geometric series
a, ar, arr,arrr (read as a times r cubed),...
in this example, a=1 and r=2.
The total sum after 30 days would be: a(1-r^n)/(1-r)
in this formula, n=30
So, total money after 30 days= 1073741823 pennies = 10737418.23 dollars

Option B: $100/day for 30 days.
Total money after 30days = 3000 dollars

So, in Option A, one would make much much more money

Answer 7

A.

Last day you get 2^29 pence, the sum of all days is 2^30-1 pence, which is more than 10 million pounds.

Edit: I read answers in $. I thought that penny is for pound, and that for $ the small coin is called 'cent'... ;-)

Answer 8

2^0+2^1+...2^29 = (2^30 -1)/(2-1)=1,073,741,823 pennies
The total amount which I'll receive at the end of 30th day in case A is $10,737,418.23, while in case B is $3000. I'll choose case B, because am controlling the money here, instead of letting it to control me ;)

Answer 9

I would be happy to take just the payment on the 30th day of option A.

Answer 10

i cant be stuffed to show working but you would have over a hundred by day fifteen with the penny one.