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On the Discounting Phenomenon and Capitalization Techniques in the Mortgage Lending Context

This paper opens with the discussion of the capitalization binomial (1 i) n and how it can be decomposed after a novel fashion into the ratio of an ascending and descending geometrical progressions,- which yields a more general formulation offering a convenient setting for the further discussion of discounting and annuity formulas. Then, in Section 2, a simple behavioral model of mortgage lenders' choice between discrete annuities and continuously compounding deposits is constructed which offers insights into the mortgage lending practices and the ensuing interpretation of the variables of the discounting formula. It follows that, in the context of the behavioral model, the standard discounting formula (annuity years' purchase for a limited period) has a forward-looking dimension which is often overlooked in traditional teaching manuals for the field. The presentation of this dimension in Section 3 helps to visualize the different inter-temporal efficiency of equal payments from mortgage loan for the lender. Section 4 concludes by discussing the implications from previous sections having regard to the conventional teaching practices and how those can benefit from the foregoing exposition.