Inductive Linear Capital Growth through Accumulated Capital Pivot
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Vantage point: With some savings set aside at the prior credit,
what are the savings required at the next credit? Consider only the
next expense for each group of expenses.

Base Case: There are zero dollars saved. Consider the linear growth
function in savings required for each future expense. At next credit,
the sum of all linear growths at that point in time are how much
should be saved.

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Inductive Case: There are previously accumulated savings. Using the
prior savings as a pivot, the linear growth function provides the
savings required for each future expense at the next credit. The
sum of linear growths is all the information that is required to
be retained from the prior accumulated savings, and can be decomposed
into individual linear growths. Then at next credit, the sum of all
linear growths at that point in time are how much should be saved.

Deviations: If at the next credit there is insufficient savings to
match the required savings, then the following credit will adjust
accordingly, making up the shortfall through using the credit with
insufficient savings as the pivot and determining a new savings
origin.

Usage: See bound-capital.R (really), and test.{sh,yaml} for example input

Depends: R; yaml & docopt R libraries

TODO:
  - Determine what's going on with [./bound-capital.R -a 2000 <capital.yaml]
  - just return costs in bound_capital if savings > costs
  - Display free capital in output as well