  Quantum models based on the mathematics of quantum mechanics (QM) have been
developed in cognitive sciences, game theory and econophysics. In this work a
generalization of credit loans is introduced by using the vector space
formalism of QM. Operators for the debt, amortization, interest and periodic
installments are defined and its mean values in an arbitrary orthonormal basis
of the vectorial space give the corresponding values at each period of the
loan. Endowing the vector space of dimension M, where M is the loan duration,
with a SO(M) symmetry, it is possible to rotate the eigenbasis to obtain better
schedule periodic payments for the borrower, by using the rotation angles of
the SO(M) transformation. Given that a rotation preserves the length of the
vectors, the total amortization, debt and periodic installments are not
changed. For a general description of the formalism introduced, the loan
operator relations are given in terms of a generalized Heisenberg algebra,
where finite dimensional representations are considered and commutative
operators are defined for the specific loan types. The results obtained are an
improvement of the usual financial instrument of credit because introduce
several degrees of freedom through the rotation angles, which allows to select
superposition states of the corresponding commutative operators that enables
the borrower to tune the periodic installments in order to obtain better
benefits without changing what the lender earns.
