The problem: About 750,000 Coloradans are saddled with nearly $28 billion in student loan debt, according to the state attorney general’s office.

One solution: Ask local mathematicians how to most cost-effectively pay off the debt.

Yu-Jui Huang, an assistant professor in applied mathematics at CU, collaborated on a study with Paolo Guasoni, head of mathematical sciences at Dublin City University in Ireland to figure out the best way for borrowers to pay off ever-increasing student loan debt. Saeed Khalili, CU research assistant in the math department, supported the study, which was published in the Society for Industrial and Applied Mathematics journal this year.

Of the 750,000 Coloradans weighed down by student debt, more than 100,000 are in default and not making their loan payments, Kelsey Lesco, Colorado student loan ombudsperson with the state attorney general’s office, said.

“We often think about student debt as just a financial problem, but it’s a human problem,” Lesco said. “People aren’t just in debt. They’re delaying marriage. They’re not able to have kids. They’re not able to pass a credit check to get a job. It’s a huge problem.”

Huang and his colleagues used mathematical modeling to calculate the most cost-effective strategy to pay back student loans. Guasoni, originally from Italy, and Huang, who grew up in Taiwan, said they are from countries in which student debt is virtually non-existent. Watching the college debt burden grow in the United States was of interest to both mathematicians, they said.

Student loan debt in the U.S. surpassed $1.7 trillion in 2021, eclipsing auto loans and credit cards among the financial burdens weighing on tens of millions of Americans, according to data from the Federal Reserve. That debt has a ripple effect, causing borrowers to delay buying homes and starting families.

“It is quite remarkable the level of debt in which the new generations are being left as they graduate with college — a level of debt which has never been had in any other society,” Guasoni said. “There is a lot of misunderstanding about the way these loans work, and there isn’t enough information about how one should manage these loans.”

Guasoni and his team got to work filling the information gap.

They found that income-based repayment plans, options that set your monthly federal student loan payment based on income and family size, are not always in the borrower’s best interest.

“The optimal strategy for some borrowers is to pay down a lot at the beginning of the loan term and defer enrolling in an income-based repayment plan until a later date,” Guasoni said. “It’s a simple change in strategy, yet just like renewing a mortgage to take advantage of a lower interest rate, it can make a huge difference, resulting in tens of thousands of dollars in savings over time.”

This option is most beneficial to students with large loans, Huang said, such as those with advanced degrees in programs like dental, medical or law school who tend to carry more than $100,000 in debt.

Various loan forgiveness programs also are available, promising to forgive the remaining balance on qualifying loans if borrowers meet certain eligibilities and make consistent payments, but Guasoni said by the time the government forgives the loans — sometimes decades after graduation — the balance can balloon to more than $1 million from compounding interest and will be subject to income tax exceeding 40%.

“The year you have your student loan forgiven, you actually have to pay taxes as if you received the forgiven amount as income that year,” Guasoni said. “If you let your student loan increase over time, the amount you’re going to owe in taxes is so large, you would have been better paying off the loan more quickly to begin with. For large student loans, such taxes can reach hundreds of thousands of dollars.”

The exact calculation that allows borrowers to plug in the terms of their loan can be found in the scholars’ journal article. 

The formula uses the loan term, income tax rate, interest rate of the student loan and interest rate of the borrower’s next most expensive loan to calculate a number. If the number is negative, the mathematicians suggest enrolling in an income-based repayment plan immediately. If positive, it equals the number of years to wait before enrolling in a plan, understanding that the borrower should pay down as much as possible in the meantime.

As an example, the researchers considered a dental school graduate carrying $300,000 in debt at the usual 7.08% interest. Keeping up maximum payments based on an assumed $100,000 starting salary to repay the loan as quickly as possible yields an overall loan cost of $512,000, researchers found. Enrolling in an income-based repayment plan immediately to keep the payments lower yields a total loan cost of $524,000 when taxes on the forgiven amount are accounted for. Using the formula proposed by the researchers yields the lowest total loan cost of $490,000 — a $34,000 savings.

Huang noted that if a student loan is less than $50,000, it’s likely more cost-effective to hold off enrolling in an income-based plan, if possible.

Megan Smith, a Denver physical therapist, said she owes more than $100,000 in student loans after completing her undergraduate degree in Minnesota and her doctor of physical therapy degree at the University of Colorado Anschutz Medical Campus in 2016.

“It’s an astounding and almost unreal amount of money,” Smith said. “When you’re younger, the student loans you’re accepting feel like fake money. It doesn’t really register what it’s going to entail. You’re just signing up for them to complete the next step in going to college.”

Smith pays more than $500 a month toward her student loans through the income-based payment plan. Without that plan, she said, her monthly payments would exceed what she pays in rent.

“I don’t even pay enough to make a dent,” Smith said. “I owe more now than I did when I graduated.”

The mathematicians’ research notes that while student loans can expand access to higher education, recent studies have found higher balances of student loans contribute to a reduction in home ownership and entrepreneurship, delayed marriages, postponed parenthood and an increase in moving back in with parents.

“Also controversial is the interaction between student loans and tuition,” the research paper said, adding that research has shown an increase in student loans leads to an increase in tuition. “Thereby suggesting that colleges (rather than students) may be the beneficiaries of a large fraction of government loan subsidies.”

Thomas Hernandez, interim executive director of financial aid and scholarships at Metropolitan State University of Denver, would like to see more financial literacy education at the high school level. In the meantime, he said it’s imperative for colleges to educate students about their financial aid, particularly at institutions such as MSU Denver in which so many students are first-generation college attendees.

Any student who borrows a federal loan must complete a counseling course at MSU Denver to help them understand what they’re signing up for, and the institution also holds financial literacy courses throughout the year.

The state also encourages borrowers with questions or concerns about their student loans to contact Lesco and her colleagues at the state attorney general’s office.

“Asking a 21-year-old to make a big life decision when they don’t really understand the big life decision is not great,” said Smith, who feels like traditional rites of passage such as home ownership are quashed by her student debt. “I wish I had known more about what I was getting into.”

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