Take 1$ (in ANY base: 10, 8, 2...)
Now, assume that interest is 10%

write down the numbers for the years 0 through 4
Now write down the nCr pyramid next to it (pascales triangle?)

See any resemblance?

Code:
1
1.1
1.21
1.331

   1
  1 1
 1 2 1
1 3 3 1
Oh, by the way, I know why it works.