## Abstract

Use of a promise to pay by a bank to insure an outstanding loan in order to return the value of the insured amount into capital for use in writing a new loan is an invention in banking with calculably greater potential economic impact than the original invention of reserve banking. The consequence of this lending invention is to render the existing money multiplier equations of reserve banking obsolete whenever it is used. The equations describing this multiplier do not converge. Each set of parameters for reserve percentage, nesting depth, etc. creates a unique logarithmic curve rather than approaching a limit. Thus it is necessary to show behavior of this new equation by numerical methods. It is shown that remarkable multipliers occur and early nesting iterations can raise the multiplier into the thousands. This money creation innovation has the demonstrated capacity to impact nations. Understanding this new multiplier is necessary for economic analyses of the GFC.

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