Researchers find optimal way to repay student loans

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After graduating or leaving college, many students are faced with a difficult choice: try to pay off their student loans as quickly as possible to save on interest, or sign up for an income-based repayment plan. , which offers affordable payments based on their income and forgets any remaining balance after 20 or 25 years.

There are pros and cons to each option, and trying to discern the best path can be daunting. This is why Yu-Jui Huang and Saeed Khalili of the University of Colorado Boulder, a former graduate student in financial mathematics, as well as Paolo Guasoni of the University of Dublin City, decided to look into the problem a bit.

Researchers have developed a new mathematical model to determine the optimal student loan repayment strategy, based on a borrower’s particular circumstances. In April, they published an article describing their approach in the SIAM Journal of Financial Mathematics.

Instead of choosing one of these separate options and sticking to them, some borrowers should consider combining the two to create their own hybrid repayment strategy, the researchers found.

“The rule of thumb is that if your balance is really small, pay it off as quickly as possible, and if your balance is large, enroll in an income-based program immediately,” said Huang, assistant professor at CU. Boulder. Applied Mathematics which specializes in mathematical finance and applied probability.

“We find that in between those two extremes there is actually a third strategy, which is that you should pay as much as possible in the first few years. And after that, switch to an income-based repayment program.”

The model incorporates fundamental math, Huang said, but is probably the first of its kind for student loans. Previous studies were mostly empirical, estimating the actual effects of student loans on the economy and on individual borrowers. Very little research has been done from a mathematical perspective on the best strategy a student borrower should employ, he said.

Researchers saw an opportunity to contribute to the academic literature while helping borrowers make sound repayment decisions. Student loans now total around $ 1.7 trillion and affect nearly 45 million borrowers in the United States, hampering their ability to buy homes, start businesses and attend higher education.

“We made the model as simple as possible,” said Huang. “For many students, it can save them money.

The model takes into account that borrowers must pay income tax on any loan amount canceled under an income-based repayment plan, as well as compound interest rates on various loans. students. It helps borrowers determine when to stop making regular payments and switch to an income-based repayment plan, a time called the critical time horizon.

“The critical horizon is when the benefits of forgiveness match the costs of capitalization,” the researchers write.

Already, researchers are thinking about ways to improve their model. On the one hand, they hope to incorporate more randomness into the model, which currently requires borrowers to make their best estimate of their future income level, tax rate, and living expenses. They also want to consider lifestyle changes that may affect borrowers’ motivation to repay student loans, such as getting married, buying a house, and having children.

“In practice, what people say is, ‘Yes, I’m going to be a dentist. Looking at the past data, I know my starting salary should be this and after a few years my salary should be this. get to that particular stage and so on, “Huang said.” The point of introducing randomness here is that some dentists get really rich in five or 10 years, and some don’t. Even if you look at the data, you cannot be sure which category you will eventually fall into. in.”

While the researchers themselves do not intend to turn their formula into some kind of widely accessible calculator, they are open to existing student loan repayment calculators that adopt their model so that I can help so many borrowers. as possible.

“At the moment, the students don’t really have concrete or rigorous guidelines – they may just have these general impressions, but there is no calculation to justify them,” Huang said. “We created a simple model, but one which underwent very rigorous mathematical treatment.”

Finding the best way to pay off student debt

More information:
Paolo Guasoni et al, Short Communication: American Student Loans: Repayment and Valuation, SIAM Journal of Financial Mathematics (2021). DOI: 10.1137 / 21M1392267

Provided by the University of Colorado at Boulder

Quote: Researchers Find Optimal Way to Pay Off Student Loans (2021, June 18) retrieved June 18, 2021 from

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