Ponder This Challenge - April 2001 - College saving account

(Inspired by a problem by Kenneth Wilke.)

A man has two children.
He opens college savings accounts for each of them, starting each with seven dollars and fifty cents.
(From what he remembers of tuition, he thinks that this will be helpful.)

Then the rigorous savings plan begins.
During the first month he deposits some positive amount (dollars and cents) into the son's account.
During the second month he deposits some positive amount into the daughter's account.
During the ensuing months he continues to alternate between the accounts, but from the third month onward the amount of each deposit is equal to the sum of the previous two months' deposits. (So the son's deposit during the third month is the sum of the son's desposit in the first month plus the daughter's deposit in the second month.)

The accounts bear no interest.
(This is another clue into the man's naivete.)

At the end of two years and four months, the daughter is a millionaire (exactly).
How much does the son have in his account (exactly)?
What colleges will he be able to afford?

Solution

• Click here to view the solution

  $618,042.45.  

  Any college on the planet.

  Each penny deposited to the son's account in the first month eventually causes a total of $1,964.17 in his account and$3,178.11 in the daughter's account.

  Each penny deposited to the daughter's account in the first month eventually causes a total of $1,964.17 in her account and$1,213.94 in the son's account.

  If the initial deposits are x cents and y cents, the daughter's wealth tells us that
  3178.11x + 1964.17y + 7.50 = 1000000.00,
  whose only solution (in positive integers) is x=73, y=391.

  The son's wealth is then
  1213.94*391 + 1964.17*73 + 7.50 = 618,042.45.

  The monthly deposits are

  3.91, 0.73, 4.64, 5.37, 10.01, 15.38, 25.39, 40.77, 66.16, 106.93, 173.09, 280.02, 453.11, 733.13, 1186.24, 1919.37, 3105.61, 5024.98, 8130.59, 13155.57, 21286.16, 34441.73, 55727.89, 90169.62, 145897.51, 236067.13, 381964.64, 618031.77.

  ---

  If you have any problems you think we might enjoy, please send them in. All replies should be sent to: ponder@il.ibm.com

Solvers

• Yuriy Groysman (04.02.2001 @ 11:17 AM EDT)
• Samantha Levin (04.02.2001 @ 12:19 PM EDT)
• Al Zimmermann (04.02.2001 @ 12:32 PM EDT)
• Marian Olteanu (04.02.2001 @ 2:12 PM EDT)
• Jayavel Sounderpandian (04.02.2001 @ 2:23 PM EDT)
• Richard Doane (04.02.2001 @ 2:27 PM EDT)
• Brian Bitto (04.02.2001 @ 2:32 PM EDT)
• Guenter Mair (04.02.2001 @ 3:02 PM EDT)
• Sunil Srivastava (04.02.2001 @ 3:56 PM EDT)
• Tim Edmonds (04.02.2001 @ 4:51 PM EDT)
• Christie Bolton (04.02.2001 @ 5:01 PM EDT)
• Ross Millikan (04.02.2001 @ 5:20 PM EDT)
• Colin Bown (04.02.2001 @ 6:41 PM EDT)
• Mark Lodermeier (04.03.2001 @ 12:03 AM EDT)
• Ether Jones (04.03.2001 @ 1:31 AM EDT)
• Dharmashankar Subramanian (04.03.2001 @ 1:33 AM EDT)
• K V Manjunath (04.03.2001 @ 2:23 AM EDT)
• Prithu (04.03.2001 @ 2:42 AM EDT)
• Kavitha Govindan (04.03.2001 @ 6:19 AM EDT)
• Juraj Lorinc (04.03.2001 @ 6:33 AM EDT)
• Caspar Addyman (04.03.2001 @ 8:46 AM EDT)
• Chris Reedy (04.03.2001 @ 9:25 AM EDT)
• Elazari Amit (04.03.2001 @ 9:36 AM EDT)
• Dmitri Asonov (04.03.2001 @ 9:50 AM EDT)
• Aron Fay (04.03.2001 @ 10:06 AM EDT)
• Henry Bottomley (04.03.2001 @ 10:12 AM EDT)
• Dave Biggar (04.03.2001 @ 12:15 PM EDT)
• Jimmy Hu (04.03.2001 @ 2:17 PM EDT)
• Francis Golding (04.03.2001 @ 3:37 PM EDT)
• Grant Meynell (04.03.2001 @ 3:48 PM EDT)
• Chad Dickey (04.03.2001 @ 4:33 PM EDT)
• Philippe Fondanaiche (04.03.2001 @ 7:01 PM EDT)
• Stephane Higueret (04.04.2001 @ 2:19 AM EDT)
• Krishna Kumar (04.04.2001 @ 9:32 AM EDT)
• Juan Ivaldi (04.04.2001 @ 10:16 AM EDT)
• Marco Aiello (04.04.2001 @ 6:12 PM EDT)
• Alan Skelley (04.04.2001 @ 7:28 PM EDT)
• Lance Nathan (04.05.2001 @ 3:44 AM EDT)
• Michael Malak (04.05.2001 @ 3:15 PM EDT)
• Vince Lynch (04.05.2001 @ 4:19 PM EDT)
• Donna Carroll (04.05.2001 @ 4:20 PM EDT)
• Bill Schwennicke (04.05.2001 @ 4:30 PM EDT)
• Rocke Verser (04.06.2001 @ 6:36 AM EDT)
• Sean Blanchflower (04.06.2001 @ 8:45 AM EDT)
• Mark Abramson (04.06.2001 @ 9:07 AM EDT)
• Peter Huesken (04.06.2001 @ 11:10 AM EDT)
• Josh Horwich (04.06.2001 @ 4:54 PM EDT)
• Douglas Schrag (04.07.2001 @ 11:34 AM EDT)
• Darryl Buller (04.07.2001 @ 4:49 PM EDT)
• Denis Borris (04.08.2001 @ 12:05 AM EDT)
• Rich Bauer (04.08.2001 @ 2:49 PM EDT)
• Marijke van Gans (04.08.2001 @ 10:16 PM EDT)
• Subramanian (04.09.2001 @ 7:10 AM EDT)
• Mitchell Kaplan (04.09.2001 @ 12:15 PM EDT)
• Carl Huber (04.11.2001 @ 12:14 AM EDT)
• Sudipta Das (04.11.2001 @ 10:05 AM EDT)
• Steven Huntington (04.11.2001 @ 1:19 PM EDT)
• Tamas Visegrady (04.12.2001 @ 6:07 PM EDT)
• Mark Pilloff (04.13.2001 @ 4:58 PM EDT)
• Rick Brewster (04.14.2001 @ 6:41 AM EDT)
• Sameer Pawanekar (04.16.2001 @ 5:18 AM EDT)
• Derek Kisman (04.16.2001 @ 2:02 PM EDT)
• Nis Jorgensen (04.16.2001 @ 4:45 PM EDT)
• Steve Walter (04.16.2001 @ 5:18 PM EDT)
• Yosi Harshoshanim (04.17.2001 @ 7:43 AM EDT)
• Ming Song (04.17.2001 @ 3:52 PM EDT)
• Matt Johnson (04.17.2001 @ 9:24 PM EDT)
• Cristi Oftez (04.18.2001 @ 4:04 PM EDT)
• Michael Jacquemin (04.19.2001 @ 8:06 AM EDT)
• Tim Atkinson (04.19.2001 @ 10:54 AM EDT)
• Paul Kahler (04.19.2001 @ 3:26 PM EDT)
• Arjun Viswanathan (04.19.2001 @ 6:35 PM EDT)
• William Webb (04.20.2001 @ 1:38 AM EDT)
• Adeel Shah (04.21.2001 @ 6:56 PM EDT)
• Diego M.S. Erdody (04.21.2001 @ 12:08 AM EDT)
• Paul Van den Keybus (04.23.2001 @ 3:42 PM EDT)
• Ravishankar Arunachalam (04.23.2001 @ 8:54 PM EDT)
• (04.23.2001 @ 8:54 PM EDT)
• Ionel Santa (04.24.2001 @ 3:02 PM EDT)
• Steve Elkins (04.30.2001 @ 4:53 PM EDT)