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Explicitly Stated (Posted on 2004-08-18) Difficulty: 3 of 5
A certain bank doesn't believe in interest and gives none the whole year. However, they do two things as a gift at the end of the year. They put money into your account such that it has 5 times as much as it did before. Then, they put 8 dollars in the account after that.

Jack gets one of these accounts at the start of year 1, and puts in 6 dollars. Assuming there are no other withdrawals or deposits into that account, figure out how much money is in that account at the beginning of year x, even if you don't know how much was in the account any of the previous years.

For example, on the beginning of year 1, he would have 6 dollars. On the beginning of year 2, he would have 38 dollars, and on the beginning of year 3 he would have 198 dollars.

What if you put in A dollars to start at the beginning of the first year, the bank put money into your account at the end of the year such that it was B times as much as before, and then put in C more dollars after that; how much money would you have at the beginning of year x, assuming everything else is normal and there are no withdrawals or deposits, even if you don't know how much was in the account any of the previous years?

No Solution Yet Submitted by Gamer    
Rating: 4.0000 (5 votes)

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Solution Try | Comment 7 of 11 |

Gotta go so I'll do this quick.

((B^x )- 1) * ( (B-1) * A + C ) + A

Since f(n) = f(n-1)*b + c, the value increases by (b-1)*f(n-1)+c each time, or (b-1)*a+c the first time, ( (b-1)*a+c ) * b the second time, ( (b-1)*a+c) * b^2 the third time, and ( (b-1)*a+c) * (b^n-1) the n'th time. Summing all of these up, you get one less than B^n  {(b-1)*a+c} increases over the original A, or

((B^x)-1) * ((B-1)*A +C) + A

The explaination could be clearer, sorry.

  Posted by Rajal on 2004-08-18 18:05:01
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