# Finding the best way to pay off student debt

The student loan burden in the United States continues to grow unabated, currently accounting for a total of $ 1.7 trillion in household debt on nearly 45 million borrowers. “The introduction of income-based repayment over the past decade has made student loans rather complicated,” said Paolo Guasoni of Dublin City University. As borrowers navigate this complex process, they face long term consequences; people with education debt are less likely to own a home or become an entrepreneur, and generally postpone enrollment in higher or professional education. Although legislative reform is needed to tackle this large-scale problem, individual borrowers can take steps to repay their loans with minimal long-term costs.

In an article published in April in the *SIAM Journal on Financial Mathematics*, Guasoni – with Yu-Jui Huang and Saeed Khalili (both from the University of Colorado, Boulder) – developed a strategy to minimize the overall cost of paying off student loans. “In the literature, we mostly found empirical studies discussing what borrowers do,” Huang said. “But what we wanted to know was rather how *should* will a borrower repay to minimize the debt burden? ”

Students become responsible for repaying their loans a few months after graduation or deregistration, and face an increase in the loan at a national fixed interest rate. One option for borrowers is to repay their balance in full by a *fixed maturity* – the date on which the final payment of a loan is due. Another is to join an income-based scheme, in which monthly payments are only due if the borrower has income above a certain subsistence threshold. If payments are required, they are proportional to the amount the borrower makes above that threshold. After about 20 to 25 years, any remaining balance is written off but taxed as ordinary income. “The tension is between deferring payments until forgiveness and letting interest inflate the loan balance over time,” Guasoni said. The fiscal cost of deferring payments increases exponentially with longer delays to remittance, potentially offsetting the supposed savings.

The intuitive approach for many borrowers may be to pay off small loans as quickly as possible, as even minimal payments would extinguish the balance at the end of its term, making forgiveness unnecessary. Likewise, one may wish to minimize payments for a large loan through an income-based system, especially if the loan will be canceled in a few years anyway. However, the situation is not always as simple as it seems. “The counterintuitive part is, if your loan is large and the forgiveness is far, it may be best to maximize payments in the early years to keep the loan balance from exploding,” Huang said. “Then you can switch to income-based repayment and enjoy the forgiveness.”

To determine what really is the best way to pay off a student loan, the authors created a mathematical model of a borrower who took out a federal student loan – the most common type of student loan – with a constant interest rate. The model assumes that the borrower is able to repay the loan according to its original term and possibly even make additional payments; otherwise, they would have no choice but to enroll in an income-based plan. Paying off the loan quickly helps reduce compound interest costs. However, the borrower’s motivation to do so is contradicted by the possibility that the remaining balance will be written off and taxed in the future, which encourages them to delay payment until the remission date.

The mathematical model revealed several possible approaches for a borrower who wishes to minimize the overall cost of their loan. “The optimal strategy is to (i) repay the loan as quickly as possible [if the initial balance is sufficiently low], or (ii) maximize payments up to a *critical horizon* (maybe now) and then minimize them through an income-based refund, “Guasoni said. The critical horizon comes when the benefits of the discount start to outweigh the costs compounded by interest on the balance of the loan. For large loans with a high interest rate – which are common for professional degrees – the savings from the strategy of high upfront payments followed by enrollment in an income-based plan can be substantial. , for those who are able to afford such a diet.

The authors gave an example of a dental school graduate with a balance of $ 300,000 in Direct PLUS loans with an interest rate of 7.08% (according to the American Dental Education Association, 83% of dental school graduates have student loan debt, with an average balance of $ 292,169). This graduate has a starting salary of $ 100,000 which will increase by four percent per year, and is able to repay no more than 30 percent of the income he earns above the subsistence level. If they kept those maximum payments, they would pay off the loan in less than 20 years at a total cost of $ 512,000.

The graduate example could also immediately enroll in an income-based rebate, paying only 10 percent of the income they earn above subsistence. After 25 years, their balance would equal $ 1,053,000 due to compound interest. This balance would be forgiven and taxed as income at a rate of 40 percent, resulting in a total cost of $ 524,000. Alternatively, the graduate could use the strategy suggested by the authors and repay 30% of their over-subsistence income for about nine years, then switch to the income-based repayment system. The remaining balance to be forgiven after 25 years would then be $ 462,000, resulting in a total cost of payments and taxes of $ 490,000 – the lowest of all strategies. The reduction in the balance over several years of high payments slows down the resulting balance growth during the period of minimum payments.

Future research may further explore the more complex factors of student debt repayment. The authors’ model is deterministic – it ignores the fact that interest rates could potentially change in the future. However, interest rates can go up or down, which can force borrowers to refinance or delay payments. More work is needed to determine the influence of these changes on optimal debt repayment.

This research has shed light on how borrowers’ choices in repaying their loans can have a dramatic impact on overall costs, especially given compound interest. “If you have student loans, you should carefully consider your specific options and see what the total cost would be under different strategies,” Guasoni said. Huang agreed, noting that the proposed strategy could be particularly beneficial for large loans that are often held by graduates of law and dental schools. “Each loan is slightly different,” he said. “Our model doesn’t capture every detail possible, but it helps focus attention on two possibilities: the fastest full repayment or enrollment in an income-based plan, possibly after a period of high payments.” Careful and mathematical examination of the approach to loan repayment can help borrowers make decisions that will benefit them in the years to come.

**Source article:** Guasoni, P., Huang, Y.-J., and Khalili, S. (2021). American student loans: repayment and evaluation. *SIAM J. Finan. Math., 12*(2), SC-16-SC-30.

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