Here is the math secret of the cheapest student loan repayment strategy



Problem: According to the state attorney general’s office, about 750,000 Colorado residents have nearly $ 28 billion in student loan debt.

One solution: ask local mathematicians what is the most cost-effective way to pay off the debt.

Yu-Ju Huang, assistant professor of applied mathematics at CU, collaborated with Paolo Guasoni, head of mathematics at City University Dublin in Ireland, to figure out how borrowers can best pay off their ever-growing student loan debt. Said Khalili, Research Fellow at the Department of Mathematics at CU, supported the research that was published in Journal of the Society for Industrial and Applied Mathematics this year.

Of the 750,000 Colorado residents suffering from student debt, more than 100,000 of Colorado’s 750,000 residents are in default and are not making loan payments, according to Kelsey Lesko, the student loan officer at the Colorado attorney general’s office.

“We often think of student debt as a financial problem, but it’s a human problem,” Lescaut said. “People are not just in debt. They postpone marriage. They cannot have children. They cannot pass a credit check to get a job. This is a huge problem. “

Huang and colleagues used mathematical modeling to calculate the most cost-effective student loan repayment strategy. Guasoni, who hails from Italy, and Huang, who grew up in Taiwan, said they were from countries with little to no student debt. Both mathematicians were interested in the rise of the college debt burden in the United States, they said.

According to the data, US student loan debt surpassed $ 1.7 trillion in 2021, eclipsing auto loans and credit cards among the financial burden on tens of millions of Americans. Federal Reserve data… This debt has a ripple effect, forcing borrowers to delay buying houses and starting families.

“The level of debt that leaves new generations of college graduates is remarkable enough — a level of debt that has never been found in any other society,” Guasoni said. “There is a lot of misunderstanding about how these loans work and there is not enough information on how these loans should be managed.”

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

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

“The optimal strategy for some borrowers is to pay a larger amount at the start of the loan term and postpone registration for an income-based repayment plan at a later date,” Guasoni said. “It’s a simple change in strategy, but just like extending a mortgage to use a lower interest rate, it can make a huge difference, resulting in tens of thousands of dollars in savings over time.”

According to Huang, this option is most beneficial for students with large loans, such as advanced degree students in programs such as dental, medical, or law school, who typically have more than $ 100,000 in debt.

Various loan forgiveness programs are also available, promising to write off the balance of eligible loans if borrowers meet certain qualifications and make consistent payments, but Guasoni said that by the time the government forgives loans – sometimes decades after issue – the balance could expand to more more than US $ 1 million on compound interest and will be subject to income tax in excess of 40%.

“In the year your student loan is forgiven you, you actually have to pay taxes as if you received the forgiven amount as income this year,” Guasoni said. “If you let your student loan grow over time, the amount you are going to owe in taxes is so large that you would be better off paying off the loan from the start. For large student loans, these taxes can run into hundreds of thousands of dollars. ”

The exact calculation that allows borrowers to specify the terms of their loan can be found in the writings of scholars. Journal article.

The formula uses the loan term, income tax rate, student loan interest rate, and the borrower’s next most expensive loan interest rate to calculate the number. If the number is negative, mathematicians suggest enrolling in an income-based repayment plan immediately. In case of a positive result, it is equal to the number of years of waiting before being included in the plan, with the understanding that the borrower, in the meantime, must pay as much as possible.

As an example, the researchers looked at a dental school graduate with $ 300,000 in debt at a regular rate of 7.08%. The researchers found that maintaining maximum payments based on an estimated starting salary of $ 100,000 to pay off the loan in the shortest possible time yields a total loan cost of $ 512,000. Immediate inclusion in an income-based repayment plan to lower repayments yields a total loan cost of $ 524,000 including taxes on the forgiven amount. Using the formula suggested by the researchers yields the lowest total loan cost of $ 490,000 – a savings of $ 34,000.

Huang noted that if the student loan amount is less than $ 50,000, it will probably be more cost effective to defer enrollment in an income-based plan if possible.

Yu-Ju Huang, Associate Professor of the Department ...

R.J. Sangosti, The Denver Post

Yu-Ju Huang, assistant professor of applied mathematics at the University of Colorado at Boulder, has been researching the most economical way to pay off student loans. Huang is pictured at his home office in Boulder on June 14, 2021.

Megan Smith, a Denver-based physical therapist, said that after completing her bachelor’s degree in Minnesota and earning her Ph.D. in physical therapy from the University of Colorado Anschutz Medical Campus in 2016, she owed over $ 100,000 in student loans.

“This is an astounding and almost unrealistic amount of money,” Smith said. “When you are young, the student loans you take seem like counterfeit money. It doesn’t really take into account what this entails. You just subscribe to them to take the next step in college. “

Smith pays over $ 500 a month on his student loans through an income-based payment plan. Without the plan, she said, her monthly payments would have exceeded her rent.

“I don’t even pay enough to make a dent,” Smith said. “Now I am in debt more than when I graduated.”

A study by mathematicians notes that while student loans may increase access to higher education, recent research has shown that higher student loan balances contribute to reduced home ownership and entrepreneurship, delayed marriages, delayed parenting, and increased home transfers.

“Also controversial is the interaction between student loans and tuition fees,” the research paper said, adding that studies have shown that an increase in student loans leads to an increase in tuition fees. “Thus assuming that colleges (not students) may be the beneficiaries of a significant portion of government grants.”


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