Hexbyte Glen Cove Researchers find optimal way to pay off student loans thumbnail

Hexbyte Glen Cove Researchers find optimal way to pay off student loans

Hexbyte Glen Cove

Credit: Unsplash/CC0 Public Domain

After graduating or leaving college, many students face a difficult choice: Try to pay off their student loans as fast as possible to save on interest, or enroll in an income-based repayment plan, which offers affordable payments based on their income and forgives any balance remaining after 20 or 25 years.

There are pros and cons to each option, and trying to discern the better path can be daunting. That’s why University of Colorado Boulder’s Yu-Jui Huang and Saeed Khalili, a former graduate in financial mathematics, along with Dublin City University’s Paolo Guasoni, decided to throw a little mathematical muscle at the problem.

The researchers developed a novel for determining the optimal student loan repayment strategy, based on an individual borrower’s specific circumstances. In April, they published a paper outlining their approach in the SIAM Journal on Financial Mathematics.

Instead of choosing one of these distinct options and sticking with it, 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, just pay it as quickly as possible, and if your balance is large, then enroll in an income-based scheme right away,” said Huang, a CU Boulder assistant professor of applied mathematics who specializes in mathematical finance and applied probability.

“We find that, between these two extremes, there’s actually a third strategy, which is, you should pay as much as possible over the first several years. And after that, switch to an income-based repayment scheme.”

The model incorporates basic, fundamental mathematics, Huang said, but is likely the first of its kind for . Past studies were mostly empirical, estimating the actual effects of student loans on the economy and on individual borrowers. Very little research has been conducted through the lens of mathematics on the best strategy a student borrower should employ, he said.

The researchers saw an opportunity to contribute to the academic literature while at the same time helping borrowers make savvy repayment decisions. Student loans now total roughly $1.7 trillion and affect nearly 45 million borrowers in the United States, hampering their ability to buy homes, start businesses and attend graduate school.

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

The model takes into account the fact that borrowers have to pay income tax on any loan amount that’s forgiven under an income-based repayment plan, as well as the compounding interest rates of various student loans. It helps borrowers determine when they should stop making regular payments and switch to an income-based repayment scheme, a point in time called the critical horizon.

“The critical horizon is the time at which the benefits of forgiveness match the costs of compounding,” the researchers write.

Already, the researchers are considering ways to improve their model. For one, they hope to incorporate more randomness into the model, which right now asks borrowers to take their best guess at their future income level, tax rate and living expenses. They also want to consider lifestyle changes that may affect borrowers’ motivation for paying off 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 past data, I know my starting salary should be this and, after a few years, my salary should grow to this particular stage and so on,'” Huang said. “The purpose of introducing the randomness here is because some dentists become really rich in five or 10 years, and some others are not so rich. Even if you look at the data, you can’t be quite sure which category you will eventually fall into.”

Though the researchers have no plans themselves to turn their formula into some sort of widely accessible calculator, they’re open to existing student loan repayment calculators adopting their model so that I can help as many borrowers as possible.

“Right now, students don’t really have any kind of concrete or rigorous guidelines—they may just have these general impressions but there’s no math to justify those,” Huang said. “We have created a simple , but one that’s undergone a very rigorous mathematical treatment.”



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

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Hexbyte Glen Cove Thin is now in to turn terahertz polarization thumbnail

Hexbyte Glen Cove Thin is now in to turn terahertz polarization

Hexbyte Glen Cove

Ultrathin, broadband polarization rotators are made possible by ultrathin carbon nanotube films developed at Rice University in 2016. The films of highly aligned single-walled nanotubes were first made in 2016. Credit: Kono Laboratory/Rice University

It’s always good when your hard work reflects well on you.

With the discovery of the giant rotation of light, that is literally so.

The ultrathin, highly aligned carbon nanotube films first made by Rice University physicist Junichiro Kono and his students a few years ago turned out to have a surprising phenomenon waiting within: An ability to make highly capable terahertz polarization rotation possible.

This rotation doesn’t mean the films are spinning. It does mean that polarized light from a laser or other source can now be manipulated in ways that were previously out of reach, making it completely visible or completely opaque with a device that’s extremely thin.

The unique optical rotation happens when linearly polarized pulses of light pass through the 45-nanometer film and hit the silicon surface on which it sits. The light bounces between the substrate and film before finally reflecting back, but with its polarization turned by 90 degrees.

This only occurs, Kono said, when the input light’s polarization is at a specific angle with respect to the nanotube alignment direction: the “magic angle.”

The discovery by lead author Andrey Baydin, a postdoctoral researcher in Kono’s lab, is detailed in Optica. The phenomenon, which can be tuned by changing the refractive index of the substrate and the film thickness, could lead to robust, flexible devices that manipulate .

Rice University physicists have made unique broadband polarization rotators with ultrathin carbon nanotube films. The films optically rotate polarized light output by 90 degrees, but only when the input light’s polarization is at a specific angle with respect to the nanotube alignment direction: the “magic angle.” Credit: Kono Laboratory/Rice University

Kono said easy-to-fabricate, ultrathin broadband polarization rotators that stand up to high temperatures will address a fundamental challenge in the development of terahertz optical devices. The bulky devices available until now only enable limited polarization angles, so compact devices with more capability are highly desirable.

Because easily passes through materials like plastics and cardboard, they could be particularly useful in manufacturing, quality control and process monitoring. They could also be handy in and for security screening, because many materials have unique spectral signatures in the terahertz range, he said.

“The discovery opens up new possibilities for waveplates,” Baydin said. A waveplate alters the polarization of light that travels through it. In devices like terahertz spectrometers used to analyze the molecular composition of materials, being able to adjust polarization up to a full 90 degrees would allow for data gathering at a much finer resolution.

“We found that specifically at far-—in other words, in the terahertz frequency range—this anisotropy is nearly perfect,” Baydin said. “Basically, there’s no attenuation in the perpendicular polarization, and then significant attenuation in the parallel direction.

“We did not look for this,” he said. “It was completely a surprise.”

He said showed the effect is entirely due to the nature of the highly aligned nanotube , which were vanishingly thin but about 2 inches in diameter. The researchers both observed and confirmed this giant polarization rotation with experiments and computer models.

“Usually, people have to use millimeter-thick quartz waveplates in order to rotate polarization,” said Baydin, who joined the Kono lab in late 2019 and found the phenomenon soon after that. “But in our case, the film is just nanometers thick.”

“Big and bulky waveplates are fine if you’re just using them in a laboratory setting, but for applications, you want a compact device,” Kono said. “What Andrey has found makes it possible.”



More information:
Andrey Baydin et al, Giant terahertz polarization rotation in ultrathin films of aligned carbon nanotubes, Optica (2021). DOI: 10.1364/OPTICA.422826

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Thin is now in to turn terahertz polarization (2021, May 20)
retrieved 21 May 2021
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