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Wed 22 Oct, 2008 04:55 pm
A successful businessman opened a retirement account by depositing a certain amount of money (some dollars, no cents) just before the end of a year. He made another deposit (again, some dollars, no cents) one year later. From that time, towards the end of each year he deposited some amount of money. His deposits followed a pattern:
From the third year onwards, the amount of each deposit was equal to the sum of the two previous deposits (from the two previous years).
His 20th deposit was $1,000,000 exactly. What was his initial deposit? Justify your answer
Note that the entire question involves only the deposits made to the savings account, thus there is no need to worry about interest calculations in your solution.
@Valedictum,
Without calculating interest, this ain't no fun.
@Valedictum,
The initial deposit was $154.
@DrewDad,
hmm how did you get that ? because what i was doing was saying at the first stage the deposit was x dollars, and the second stage was y dollars, so the third deposit was 1st Deposit + 2nd Deposit = x +y and then the fourth deposit would be x + 2y and so on but then there is only one equation with two variables hence mathematically its unsolveable ? could you show some working please ?
@Valedictum,
I wrote a program that tested all of the possibilities.
You're on the right track.
@DrewDad,
hmm but still what would happen at the end : cos i got the equation 2584x + 4181y = 1000000, but then i rearranged to the general equation of a line. So
y = (1000000-2584x) / 4181. Subbed in your answers and its correct, but how would i prove it without writing a program. hah thanks btw
@Valedictum,
It's a silly question. No business man would deposit money at zero interest. Not just yet anyway. And especially not a successful one.
@spendius,
You have not read the question. It does not say that there is zero interest.
It just doesn't matter what the interest is as all we know is that his 20th DEPOSIT is a sum of the first two DEPOSITS, so how much interest he gains does not matter. The anser is 2584x+4181y=1000000, where x is the first deposit = 154 and y is the second = 144 Thanks to @markr for the Diophantine Equation
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