Student Loan Debt Will Destroy You (If You Don't Understand It)

Here's a modern horror story in four sentences. My wife and I left graduate school 23 years ago with a combined total of $70,000 of debt. Since then, we've made $500 monthly payments for 23 years, totaling over $120,000. Today we still owe $60,000. Explain to me again why student loan debt shouldn't be cancelled. So what's the horror here? Is it the fact that Stephen Cotterill has had to spend so much for so long to pay for his education and still has so much debt remaining? Or is it the fact that this graduate student took out tens of thousands of dollars of loans and doesn't even have basic financial literacy? Perhaps a little bit of column A, lot a bit of column B. In this video, I'd like to tell you a little bit about the math of student loans and how And we'll see with a very straightforward calculation that this payment plan of $500 a month was doomed from the start. And if you have this basic bit of financial literacy, you'll be better informed when taking out loans for your education and making choices about how to repay them. And you won't end up like Socialist Steve. So yeah, in the United States, college is not free. You have to make a well-informed decision about whether or not it's worth it to pay for a particular degree in the hopes that it will be able to pay for itself through a career in the long term. Most students in the United States will attend college in the state that they live in. And for going to an in-state public college, the average annual cost is about $27,000. This is counting all of the big picture things, tuition, living expenses, supplies, all of that stuff. Of course, for the whole four-year degree, we would multiply this by four and get that for four years, a ballpark average cost would be $108,000. Of course, these are difficult costs to stomach for somebody who's in college and thus doesn't have a ton of time to be working jobs and advancing a career to pay off these sorts of costs. Keep in mind that these are averages for undergraduate degrees. Of course, our introductory problem, which we will return to, concerned graduate school, but that's not going to have an effect on how we end up doing the calculations. The simple solution to this problem is loans. A student will take out loans to pay for their education while they're getting it. And then after the fact, throughout their career, they can pay off all of their student loan debt. The loans that pay for someone's education can be given by banks or other private entities, but are very often federal loans, so they're given by the government. The thing with loans is that they accrue interest. If you take out $10,000 of loans for your undergraduate degree, by the time you're done, you'll probably still owe $10,000. It won't accrue interest while you're in school, typically. However, if you don't pay anything for your loan over the next 10 years, you will definitely Now, why is interest a thing? If you only take out $10,000, why do you need to pay back more than $10,000? Well, it's because of something called the time value of money, and because, just more generally, there are costs to lending money. First and foremost, there are, of course, the basic administrative costs of processing a loan. There's paperwork, there are letters to be sent, there are discussions to be had. You can't just give out loans by expending no effort. Secondly, if someone lends you money, of course, they have no money now. They're giving up money in the present for money in the future. There's a big opportunity cost here, because instead of loaning an undergrad student tens of thousands of dollars, a loaner could instead invest in something that may have some decent returns. They could buy stocks, they could buy cryptocurrency if that's their thing, they could buy precious metals, or they could just stuff the money under their mattress. If they did that, then guaranteed, in 20 years, their money is still going to be there. Of course, if they loan their money, there is no such guarantee. There is a risk of default. To default on your loan is to not pay it back, and so someone loaning you money is always taking that risk, that they won't actually see the money returned. All of these factors mean that nobody's going to loan you money without charging some interest. Interest makes the business of loaning money just that, a business, and it could be financially smart to loan some money and get more back in the long run. Perhaps I loan $100 to a friend that he promises to pay back in a year, but because I'm giving up the $100 now, I'm hoping to get maybe $120 back in a year. As someone loaning, if I don't have the money now, I'm giving up the opportunity to invest it or buy things that I like, so I definitely want to see a little bit of extra given back. So then, how is this interest on money calculated? Well, it depends. There's one common type of interest called compound interest. This is what you get on credit card debt, and if you put money in a savings account, for example, it will accrue compound interest. For example, let's say a bank offers saving accounts with 1% interest rates that are compounded monthly. This means if I put $100 into the savings account, then after one month, this is going to be multiplied by 1 plus the interest rate of 1%, but it's going to be divided by 12 because it's compounded monthly. So basically, each month, we're going to get a 12th of 1% of the money in our account added to the account. When you look at this calculation, you see this number is the principal amount that was originally in the account. The multiplication by 1 just keeps that principal amount, but then this part is going to give us that extra that we get from the interest. In this case, a 12th of a percent times 100 is about 8 cents. So at the end of the first month, we would have $100.08. The great thing about compound interest is that after the second month, I would have that amount that was in our account at the end of the first month, $100.08, now getting multiplied by this same thing. So now we're earning interest on the interest that we earned. We're compounding interest. And as time goes on, this amount of monthly interest we're earning is going to increase because the interest is compounding. In this case, because the initial amount in the account, 100, and the interest rate of 1% are both quite small, we're not going to make a ton of money. But indeed, after 248 years, we would be earning $1 a month in interest. At this point, our account, which began with a measly $100, would have grown to about $1,200. On the other hand, if we took the initiative of adding $50 to our account each month, trying to save up money, we would actually hit $1 of monthly interest after only 22 years. Still a long time, but much less than 248. So this method of interest compounding on interest can result in some pretty rapid growth if you're actively saving money or if you're actively accruing debt. If we were to graph the amount of money in a savings account subject to compound interest, it will look something like this. You see this exponential growth. Now you may think this would start to explain Socialist Steve's situation. He must be accruing interest on interest on his debt, and thus it's really difficult to pay down. But that's not quite what's happening. Because, in fact, student loans from the government are generally simple interest. If a sum of money is accruing simple interest, it's not possible to earn interest on the interest. Simple interest only has interest calculated on the original principal amount of money. Keeping in mind the numbers from our previous example, if we had $100 in a savings account that was accruing simple interest of 1%, the calculation for two months of interest would look like this. We have 1% divided by 12 because we're doing this calculation monthly. And then if two months have passed, we would just multiply that interest number by 2. So what you see here is that this interest is only ever going to hit that principal amount of 100. If we let the 100 sit in the account for 48 months, this too would just be 48. But again, the interest here is only hitting the principal amount. As opposed to the compound interest situation, where after one month we had 8 cents of interest, and now we need to consider that in our calculation. That's now accruing interest also. These numbers are small enough that at first the numbers appear similar. After two months, we would have $100 and 16 cents. We've earned 8 cents of interest each month. But unlike the compound interest situation, we're going to keep earning 8 cents of interest because the principal amount was 100. We're only ever going to earn 8 cents of interest per month. So this is how student loan interest is calculated. It's simple interest. The only difference is that it's generally accrued daily. So whatever the principal amount of the loan was, it would be getting multiplied by 1 plus the interest rate of i, divided by 365. And this would get multiplied by, let's say, d, the number of days that have passed since interest began accruing. So when you're paying off a loan like this, you have to pay off all the interest, and you have to pay off the initial loan amount, which is called the principal. But the interest isn't getting added to the principal. So the interest isn't earning interest on itself. So this principal amount, as long as you keep making reasonable payments, is only going to go down. And as you pay off the principal, the amount of interest being accrued will reduce. But there is a key phrase there. The monthly payment you're making does need to be reasonable. So we're talking about monthly payments. Like we said, the interest is generally accrued daily, but then it would be added to your balance in total each month. But what do we mean by a reasonable monthly payment? Well, imagine the $100 we've been talking about. Instead of being in a savings account, let's say that this is your debt that is accruing simple interest. Like we said, it would be accruing interest of $0.08 per month. So what wouldn't be a reasonable monthly payment would be $0.04 per month. If you were paying $0.04 per month, you're never ever going to pay off the debt. What happens after one month? Well, you pay off $0.04, but none of that's going towards the principal amount because you already accrued $0.08 of interest. And this is just covering half of that. After another month, you take on another $0.08 of interest. So now you'd have $0.12 of interest total, and then you pay another $0.04. You're not doing anything. You're not touching the principal amount at all there. So certainly a reasonable monthly payment, at the very least, needs to be bigger, at least slightly, than the monthly interest you're accruing. But if that amount of your monthly payment is only slightly bigger than the monthly interest you're accruing, then it could take a long time indeed to pay off the entire loan. All right, we now have sufficient background knowledge to do the math that Socialist Steve certainly didn't do. Stephen Cotterell's tweet about this loan situation was made in 2024. So when he says 23 years ago, that places us in the great year 2001. At this time, the government was offering a popular form of assistance in what were These were available to undergrad and graduate students, although for graduate students, the Stafford loans would actually accrue interest immediately. They wouldn't wait until the student had finished their schooling. The Stafford loans have not been offered since July of 2010, but in the year 2001, the Stafford loans were being given with a fixed interest rate of 8.19%. This is one of the nice things about the federal student loans. Even in a shifting economy, you get a loan with a fixed interest rate, so you know exactly what you're in for. Well, you do if you know the math. Okay, now what should we do? What's the relevant calculation that's going to give us some insight into Stephen Cotterell's loan? Well, we just talked about the monthly amount of interest that might accrue on a loan. So why don't we take this number and the $70,000 of debt number and calculate what the monthly interest would be. Of course, we're making some basic assumptions here just to have some simple math to get a gist of what's going on. Stephen Cotterell mentions that this is the debt between him and his wife, so who knows exactly what loans the two of them took out, but we're just going to treat this as a single number and assume that we have a Stafford loan at 8.19% interest. Now, if Stephen Cotterell's claims about his debt situation are true, when we calculate the monthly interest for this loan, it should come out to close to $500 because he's been paying monthly $500 for 23 years and has barely paid off his loan at all. He said that they still owe $60,000. Okay, so here's the calculation and we'll see what result we get. We have the principal loan amount of $70,000. Again, interest is simple interest and it's accrued daily, so we would have the interest rate of 8.19% divided by 365. Let's say one month has 31 days, so we multiply this by 31. Now let me make sure I'm clear about the numbers here. 70,000 times 1, that's just going to give us the principal amount back of $70,000. But 70,000 times this, that's going to give us the interest after one month. And that amount of monthly interest, if Socialist Steve is telling the truth, should be pretty close to $500. So let's take our trusty transparent green limited edition TI-83 Plus and punch in that calculation. 70,000 multiplied by the interest rate of 8.19%, which is .0819 as a decimal, divide by 365, multiply by the 31 days in a month. And press enter. And what do we get? $486. So after what amounts to a five second calculation, we can see that Steven's plan of paying $500 a month is a pretty terrible plan. Based on these numbers, this would be a whopping 38 year loan. That's how long it would take to repay at these rates. Steven's acting like this is some big surprise that after 23 years, they still owe $60,000. But the payment plan he's adopted is a 38 year plan. It's far more normal, just for the perspective, for a loan repayment plan to be in the realm of 10 to 30 years. And after this whopping 38 years of coughing up $500 a month, the total amount repaid would be an insane, eye-popping $230,000. More than three times the original loan amount. And perhaps even more sickening, $160,000 of that would be completely interest. $160,000 of interest. That's over twice the original amount, just in accrued interest. Of course, over time, as these small payments of $500 a month start to cut into that principal amount, this monthly interest would go down. I punched these numbers into an online student loan calculator, and it gave me some slightly different numbers. By different, I just mean different from what Steven reported. Putting in his debt amount of $70,000 with the 8.19% interest rate, it said that after 23 years of monthly payments of $500, we should have $52,000 remaining as the principal, and at this point, the monthly interest would be $355. So even at this point, those monthly payments of $500 are mostly going towards interest. So it's no surprise the principal amount is getting reduced so slowly. Now why are these numbers, the $52,000 compared to Steven's reported $60,000 remaining, why are they different? Well, it's not really relevant. I mean, there are just things about Steven's loan we don't know. We don't actually know the interest rate. We don't know the exact numbers, but certainly his numbers are plausible, as we've seen. There's also another possibility that is worth mentioning. I mentioned earlier how with simple interest, interest will not accrue on your interest. So no amount of interest goes back into the principal amount. But there are certain circumstances with some student loans where interest will be capitalized, meaning that it's put back into the principal amount and further interest calculations are done on that new principal amount. So it's possible throughout the life of this loan that Steven had some capitalizing event, so some of the interest went into the principal, and so he's getting some interest accrued on some interest. Ultimately, those little details aren't important. What is important is the big picture of interest and monthly payments on student loan debt. When you take out a loan, know what you're getting into, run the numbers, compare the monthly payments to your projected salary in the future after school, and make sure that your monthly payments are actually reasonable and will cut down the principal in an amount of time that seems acceptable. Perhaps 38 years, like this loan seems to be, is not an amount of time you want to spend making monthly payments to cut down your debt. I will say, these things are complicated, and despite my snarky tone I've taken throughout this video, I have great sympathy for undergrad students who took out loans and didn't really understand the extent of the commitments they were making. I have less sympathy for graduate students who don't do 5 second calculations to see the future, as it were, when the future is right in front of you. I mean, seriously, $500 a month for 23 years, and you still owe $60,000? Who could have seen this coming? Everybody could have seen this coming. And let me speak my poetry to your face, it's Not infinite if you ain't really into it.