ENHANCING THE SUSTAINABILITY OF QARD HASAN THROUGH THE MESBAH POINT: A MATHEMATICAL AND ETHICAL FRAMEWORK

Abstract

Qard Hasan, or interest-free benevolent loans, represent one of the most ethically significant instruments in Islamic finance, yet their operational sustainability remains a persistent challenge, particularly in formal Islamic microfinance institutions (IsMFIs). This study introduces a critique and development of the concept of the Mesbah Point–defined as the interest rate at which the present value (PV) of total interest payments under a conventional loan structure reaches its theoretical maximum. The Mesbah Point serves as a financial benchmark to estimate the institutional opportunity cost of offering Qard Hasan without violating the principles of Shari’ah. A mathematical model is derived and simulated, identifying the PV turning point under varying loan terms and interest scenarios. While direct application of this value as an upfront payment is ethically and practically problematic, the paper proposes the Investment Mesbah Points Portfolio (IMPP) as a Shari’ah-compliant institutional solution. The IMPP allows IsMFIs to generate returns equivalent to the Mesbah benchmark through halal investments, thereby ensuring sustainability without compromising ethical integrity. This research offers a novel framework that bridges financial engineering and Islamic social finance to support inclusive development.