Mathematical Simulation of Optimal Student Loan Repayment Using First-Order Linear Ordinary Differential Equation

Abstract

The PTPTN student loan is the most accessible study loan for supporting Malaysian students to pursue their studies in tertiary education. However, the loan repayment stated in the PTPTN agreement is not made accordingly. This research aims to provide a mathematical simulation for the PTPTN student loan repayment using a first-order linear ordinary differential equation. For this purpose, variable and fixed interests are considered. First, the annual repayment amount is calculated, and the interest amount is determined. With these amounts, the repayment balance is obtained after solving the linear differential equation. Then, the repayment scheme for a chosen period is prepared. After this, a mathematical simulation for different repayments with the desired repayment periods is performed to settle the loan. In addition, the repayment amount decided by students is also simulated so that the possible repayment period in completing the loan will be suggested. From these simulation results, the relationship between the repayment amount and the repayment period is reciprocal, which indicates the increase in the repayment amount will shorten the repayment period and vice versa. In conclusion, the mathematical simulation through the first-order linear ordinary differential equation provides a flexible repayment plan for settling the PTPTN student loan repayment.