.01*(2^30) = $10,737,418.20

$ 5,368,709.12

1 2 4 8 16 32 64 132 264 528 1056 2112 4224 8448 16896 33792 67584 135168 270336 540672 1081344 2162688 4325376 8650752 17301504 34603008 69206016 138412032 276824064 553648128 1107296251 TOTAL pennies

that would be (.01 * 2^29) That would equal $5,368,709.12 EDIT: The answer above is on the 30th day after the penny was deposited. Not the 31st day, which is apparently what the question wanted. the first day plus 30 days. That means the total would be (.01 * 2^30) and that would be $10,737,418.24 This assumes that by "earns doublings" you mean that the money in the account doubles daily. 0.01 0.02 0.04 0.08 0.16 0.32 0.64 1.28 2.56 5.12 10.24 20.48 40.96 81.92 163.84 327.68 655.36 1310.72 2621.44 5242.88 10485.76 20971.52 41943.04 83886.08 167772.16 335544.32 671088.64 1342177.28 2684354.56 5368709.12 10737418.24

So, on the day 1 you earn 1 penny. On day 2, you earn 2 more. On day 3, you earn 4 more. On day 4, you earn 8 more, etc. You can quickly see that on the nth day, you add 2^n pennies to your account for that particular day. That means your total earnings up to day n is the sum of the powers of 2 from 2^0 to 2^n: earnings = 2^0 + 2^1 + 2^2 + ... + 2^n Now, here's a little trick...just go with me and see where it takes us. Let's make the problem a little more general by letting r=2, so 2^n becomes r^n: earnings = r^0 + r^1 + r^2 + ... + r^n Now let's multiply both sides by (1-r): (1 - r)*earnings = (1 - r)*(r^0 + r^1 + r^2 + ... + r^n) Now look at the right side of the equation and forget about the left side for now. Expand that multiplication on the right side: = (r^0 + r^1 + r^2 + ... + r^n) - (r^1 + r^2 + r^3 + ... + r^(n+1)) ...and now distribute the minus sign so we can get rid of the parentheses... = r^0 + r^1 + r^2 + ... + r^n - r^1 - r^2 - r^3 - ... - r^(n+1) Now, if you're clever, you see where I'm going with this. We can rearrange the terms of the above equation so that everything cancels except the first and last terms! = r^0 + (r^1 - r^1) + (r^2 - r^2) + (r^3 - r^3) + ... + (r^n - r^n) - r^(n+1) = r^0 - r^(n+1) = 1 - r^(n+1) Now let's bring back the left side of this equation that we were ignoring... (1 - r)*earnings = 1 - r^(n+1) Multiple both sides by -1: (r - 1)*earnings = r^(n+1) - 1 and we solve for your earnings: earnings = (r^(n+1) - 1)/(r - 1) Ok, so, now remember the specifics of the problem we're working. We let r=2 before, so we sub 2 back in for r: earnings = (2^(n+1) - 1)/(2 - 1) = 2^(n+1) - 1 So your total earnings that you accumulated up to day n is: earnings(n) = 2(n+1) - 1 ...and n=30, so we sub 30 in for n: earnings = 2^(30+1) - 1 = 2^31 - 1 = 2,147,483,648 - 1 = 2,147,483,647 Remember this is pennies, so we have to convert to dollars. You'd make a total of: $21,474,836.47. That's a pretty sweet investment. Where do I sign up?

1 - 1 2 - 2 3 - 4 4 - 8 5 - 16 6 - 32 7 - 64 8 - 128 9 - 256 10 - 512 11 - 1024 12 - 2048 13 - 4096 14 - 8192 15 - 16384 16 - 32768 17 - 65536 18 - 131072 19 - 262144 20 - 524288 21 - 1048576 22 - 2097152 23 - 4194304 24 - 8388608 25 - 177773216 26 - 355546432 27 - 711092864 28 - 1422185728 29 - 2844371458 30 - 5688742916 add those to get 5527746913 pennies Being that 100 pennies = $1, you now have $55277469.13 Or with commas $55,277,469.13

1-1 2-2 3-4 4-8 5-16 6-32 7-64 8-128 9-256 10-512 11-1024 12-2048 13-4096 14-8192 15-16384 16-32768 17-65536 18-131072 19-262144 20-524288 21-1048576 22-2097152 23-4194304 24-8388608 25-16777216 26-33554432 27-67108864 28-134217728 29-268435456 30-536870912 Total-805306367 cents or $8,053,063.67 If what you earn doubles each day, you would have to add up the values for the amounts earned each of the thirty days to find the total amount earned after 30 days.

I agree with anonymous $8,053,063.68 Your multiplyng each day by 2 (not squaring) and then add the previous days money all the way through. OOPS I'm wrong again.