IBM Ponder This #036 · April 2001

(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

Best opened after a real attempt

To be added.