Repayment policy for multiple loans.

Yasmin Agueda Rios-Solis,Mario Alberto Saucedo-Espinosa,Gabriel Arturo Caballero-Robledo,J Alberto Conejero

doi:10.1371/journal.pone.0175782

Abstract

The Repayment Policy for Multiple Loans is about a given set of loans and a monthly incoming cash flow: what is the best way to allocate the monthly income to repay such loans? In this article, we close the almost 20-year-old open question about how to model the repayment policy for multiple loans problem together with its computational complexity. Thus, we propose a mixed integer linear programming model that establishes an optimal repayment schedule by minimizing the total amount of cash required to repay the loans. We prove that the most employed repayment strategies, such as the highest interest debt and the debt snowball methods, are not optimal. Experimental results on simulated cases based on real data show that our methodology obtains on average more than 4% of savings, that is, the debtor pays approximately 4% less to the bank or loaner, which is a considerable amount in finances. In certain cases, the debtor can save up to 40%.

Highlights

A debtor with a set of multiple loans faces the problem of simultaneously repaying them each month: home mortgages, college tuition loans, short-term credit card debts, bank overdrafts, and car loans
When the Repayment Policy for Multiple Loans (RPML) problem is solved with our model, the proximity to the optimum is 0.06 on average, and it is reached in around 600 seconds
This work presents a linear programming formulation to determine the optimal repayment policy for multiple loans. Using such a formulation shows that the repayment policy for multiple loans belongs to the NP-hard complexity class, whereas the simpler versions considered in the literature can be solved in polynomial time

Summary

Introduction

A debtor with a set of multiple loans faces the problem of simultaneously repaying them each month: home mortgages, college tuition loans, short-term credit card debts, bank overdrafts, and car loans. This problem becomes even more challenging when income is less than expected, and the debtor faces the problem of deciding which loans to prioritize. When income exceeds expectations and there is extra capital available in a particular month, the debtor faces the task of determining where to allocate this extra money. This problem is known in the literature as the Repayment Policy for Multiple Loans (RPML).

Methods

Results

Conclusion