Why is my student loan balance not going down?

Question

This will be basic for you pros, please forgive me.

I have been paying the minimum balance on my student loan all year, but the balance shown on the site has barely gone down. I assumed that this was because they make you pay the interest first, then the principal. However, when I looked at the payoff amount, it was about the same as the balance! How is this possible?

Are you still a student, or are you out of school and now in the repayment phase of your student loan? — Ben Miller, Mar 01 '16 at 15:07
Sad... nobody should be allowed to graduate without knowing enough math to understand amortization tables. Further, never make "minimum payments" on anything unless you like giving away money. Figure out how long you want to pay, how much per month you can afford, and pay that much. — Carl Witthoft, Mar 02 '16 at 14:08
@CarlWitthoft I don't know that I'd go so far as to say that for anything, but it is definitely good advice for stuff with higher interest rates. For a low-interest mortgage, though, you're likely better off paying the normal ("minimum") payment and investing the rest of what you could have afforded to pay against it. In addition to likely being able to out-earn the interest rate on the mortgage (especially since said interest is deductible,) this also leaves you with more liquid assets in case some emergency expense arises. — reirab, Mar 02 '16 at 17:54
Work it out from the other direction. The loan company does not want you owing more; they want at least the interest. That means they must charge you more than the interest. They also would like to keep extracting money from you forever. That means charging you so little that you never make any progress on paying off the loan. The monthly fee that pays the interest and hardly anything more is the minimum payment. It is not there for your convenience; it's there to maximize the amount of time you spend in debt. — Eric Lippert, Mar 03 '16 at 00:18
If they called it what it is -- the interest maximizing payment -- then you wouldn't see it as a good thing at all. That's why its called the minimum payment. — Eric Lippert, Mar 03 '16 at 00:20
@CarlWitthoft - What happened in your life that made you like this? No, I never studied anything beyond the most basic economics. Not part of my curriculum. I do have advanced calculus and diff eq. under my belt, so it's not a math issue. You? — Ken - Enough about Monica, Mar 03 '16 at 09:12
@horsehair The interest amortization problem does not quite fit in a differential equation, because changes happen at at discrete intervals rather than continuously, but you should be able to enhance your feeling for what is happening by studying the corresponding continuous problem. You have an outstanding balance that increases at a rate proportionate to its value, but has another term that decreases it at a fixed rate. The boundary conditions are that it is equal to the principal at t=0, and will be zero at the end of the loan term. — Patricia Shanahan, Mar 03 '16 at 12:36
@horsehair nothing personal, just a general observation from a seasoned statistician and analyst that economics & econometrics is one of the least-validated fields of study, ranking marginally above astrology in their ability to identify and predict events. — Carl Witthoft, Mar 03 '16 at 12:51
@CarlWitthoft: It's not a question of knowing how to do arithmetic; it's a question of knowing what arithmetic to do. If students who can do math are being graduated without understanding the most basic thing about their student loans - and they are - then how that situation came about is a good question. Why on earth would lenders, governments and for-profit schools collude to produce a system that makes financially ignorant, deeply-indebted wage slaves out of the smartest segment of the population? That's a tough one right there. — Eric Lippert, Mar 03 '16 at 15:48
@CarlWitthoft There's no need to insult the OP's situation or their completed university curricula, let alone both. — TylerH, Mar 03 '16 at 16:04
@TylerH alternatively, there's no reason to accept that any economics degree is of any value. The suggestion that one can pretend to understand any economic theory (good or bad) without understanding basic value transactions is ridiculous. Horsehair's excuse that it was "not part of my curriculum" suggests a bigger problem: failure to question, investigate, and learn — Carl Witthoft, Mar 03 '16 at 16:15
@CarlWitthoft The biggest problem here is that it's not your place to judge the OP's life. He's clearly trying to question, investigate, and learn by asking this question in the first place. If you're only interested in lecturing people on what you think they've done wrong in the past then this site is probably not for you. — TylerH, Mar 03 '16 at 16:20
@TylerH As you might have noticed, it didn't start out that way. My original comment was on the sad lack of basics for everyone. Horsehair decided to attack on the theory that he had no responsibility for learning stuff important in every day living. At that point he implicitly invites critiques of his behavior. — Carl Witthoft, Mar 03 '16 at 16:23
@CarlWitthoft - We can agree to disagree. When someone asks me for help doing something basic on their computer, I don't criticize their lack of knowledge. I just assume they're not experienced in that area, and maybe don't even care to be. — Ken - Enough about Monica, Mar 03 '16 at 16:51

Joe · Accepted Answer · 2016-03-02T20:34:44.310

123

While it's common to think of it that way - pay off the interest first, then the principal - that's not actually how your payments work over time. It's true of any one payment, though.

Interest is earned over time. It might be added on daily, weekly, monthly, or any other frequency. For simplicity's sake, let's assume it is added 1/12*(apr) once per month.

So you have a 6% loan, starting at $10,000 principal balance. That's 0.5% per month (6%/12). So each month, you owe .005*(principal) in interest.

Your first month, then, you owe:

$10,000 Principal
$    50 Interest
-------
$10,050 Total

You will always pay at least the interest every month. Some payment plans are called "interest-only"; in those, you pay only that $50 per month, and the $10,000 never goes down for the interest-only period. (Of course, eventually you have to start paying principal...)

Any amount you pay over $50 per month, either as part of your payment or as extra (and extra designated to go to principal - an important distinction), will lower that principal. That's what actually pays off the loan.

Since payments to principal reduce the total amount you owe, they also reduce the interest due. So a $100 monthly payment, with $50 going to interest and $50 to principal, would then leave you with, next month:

$ 9,950.00 Principal
$    49.75 Interest
----------
$  9999.75 Total

You'd then pay $100 again, with now $49.75 paying interest and $50.25 paying principal.

The reason people think of this as paying interest first, is in particular with some mortgages and longer term repayment plans the far majority (commonly 80%, but in some cases higher) of each payment is allocated to paying the interest on the loan. The way these plans work is that you have a fixed monthly payment for, say, 30 years - but that's at first nearly entirely interest, because you don't have to pay much principal off to eventually get the loan paid off.

For example, to pay off that loan in 30 years, you'd only have to pay $60 per month - $50 for interest initially and $10 for principal. Since that principal will slowly rise over time (as interest slowly drops), you end up paying it off. (30 years is 360 payments, or about $21,600 - so you're going to pay a lot of interest this way, of course, over 100% interest over the life of the loan).

Since you're only paying $10 to principal each month to start with, if you add even a small amount to that payment, you pay it off far faster and pay far less interest. Add $15 to your payment - $75 instead of $60 - and now you're paying $25 to principal instead of $10, meaning you now pay it off in 18 years at that payment structure and pay only a bit over $16,000 in total - saving nearly half of the interest. Add $40 ($100 per month) and you now pay it off in closer to 10 years, and pay $14,000 in total. Even just add that for the first few years, and you'll dramatically increase your payoff rate.

I recommend using a mortgage payoff calculator, like this one which I set up with the above loan, to see how things work out. It shows you the amount going to principal and interest each year, and lets you alter the payments to see how they affect things.

Here are charts of the three options, so you can see visually how your payments break down. Like above, this assumes interest is calculated and capitalized monthly (which may be an oversimplification for your loan, but it doesn't change the numbers much).

edited Mar 02 '16 at 20:34

answered Mar 01 '16 at 15:35

Joe

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Joe - thanks for taking the time. I was thinking about just paying the thing off immediately, but it looks like my payments would go down fast after just paying down some? – Ken - Enough about Monica Mar 01 '16 at 16:31
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@horsehair Well, they certainly go down more if you pay it off in one payment :) But even adding half again your monthly payment is enough to cut the length of the loan down drastically (by around half). Like I said, go to the mortgage calc and play around with payment amounts to see what different things do. – Joe Mar 01 '16 at 16:36
2

As I read the answer I was thinking this answer would be better if he talked about extra payment toward principle, since that really helps understand the relationships involved. Then I saw the graphs and was like oh, yes this is what I wanted to see! – corsiKa Mar 01 '16 at 17:53
8

It's also worth pointing out that when you have multiple loans (very common with student loans), you should always pay the highest interest loan first, regardless of principal. A lot of online finance guides recommended paying the lowest principal first because you'll "feel good" about paying them off sooner, but personally I'd rather "feel good" about saving $10,000 by waiting another year on the big loan. Of course, I'm making the assumption that your accounts are in good standing and you can afford the minimum payments of all of your loans each month (late fees > interest > principal). – Dan Mar 01 '16 at 18:41
Also.. if you have higher interest credit card debt (credit cards are often 4x-8x higher interest rate than student loans), make only minimum payments on the student loans and pay off the credit card as soon as possible. Same goes for any other interest-accruing debts (car, house, etc.) If you can't afford at least the minimum of all your bills, you should talk to a financial advisor or call the loan company to request a payment reduction immediately. – Dan Mar 01 '16 at 18:44
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Charts are excellent. Would be even better with a common y-axis to see that the latter case involves larger monthly payments (it's in the title currently). That would also allow eyeballing the relative colored areas of the charts to see that the total amount paid is decreasing with the larger monthly payment. – Byron Wall Mar 01 '16 at 18:53
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@ByronWall I thought about that, and perhaps I will adjust them. They're vertically stacked currently, which makes it less important to have a common Y axis (in particular, you probably can't see even two whole charts on your screen at once). – Joe Mar 01 '16 at 19:02
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Gotta love how kids can graduate college and not understand this... so basic yet so powerful. – WernerCD Mar 01 '16 at 19:51
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I will admit to not understanding this very well either when I had just graduated college. It wasn't for several years until I understood it well. We just don't teach practical home finances well in this country. And I graduated with an economics degree from arguably the top Econ school in the country... – Joe Mar 01 '16 at 19:53
2

@Joe Yeah, well, economics is voodoo to begin with. And I challenge your claim that you learned econ if you didn't even learn amortization tables. – Carl Witthoft Mar 02 '16 at 14:10
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@CarlWitthoft Economics is not about practical things like that... At least not as I was taught. – Joe Mar 02 '16 at 14:14
@Joe You learned nothing about how banks work, or how they make money, or lend money, or how to amortize a bond issue? – Carl Witthoft Mar 02 '16 at 14:17
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@CarlWitthoft That is not what at least my economics classes were about. Much more theoretical, except in Econometrics (which is much more technical). That would be covered in finance, not economics. – Joe Mar 02 '16 at 14:20
@Joe Great answer but I believe student loans are a bit different than the loans you discussed here. Unlike normal loans, a student loan can accrue interest for years before you start making any payments. In the OP's case he likely was paying only interest for the first few payments, maybe almost the whole year. – Matt Mar 02 '16 at 15:54
1

@Matt The OP clarified that he was no longer a student, so payments have begun already. Further, I did discuss the possibility of interest-only payments! – Joe Mar 02 '16 at 15:57
@Joe Whether or not the OP is still a student doesnt change the fact that a lot of interest may have accrued. Your discussion of interest only payments sounds like a payment plan where, until you change plans, will result in you never paying principal. This is not what im saying. Im talking about the period of time shortly after you graduate where you have thousands of dollars of accrued interest and therefore your monthly payments for the first few months dont touch the interest. It sounds like the OP has only been making payments for about a year. – Matt Mar 02 '16 at 16:06
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@Matt Interest accrued during time as a student is typically capitalized upon graduation (or some months after graduation); at that point it becomes part of the principal, effectively. (Note he's talking about his payoff balance not being reduced, which is exactly what that would imply.) It's been a while since I was in school, but when I was, you had the options of an interest-only plan by default for the first ~6 months (where you paid just the interest on your principal) and then starting a proper principal+interest plan; that's still an interest-only plan, just a short one. – Joe Mar 02 '16 at 16:08
@Joe the OP's terminology is a bit confusing and your interpretation might be correct. Im reading "balance" to mean principal and "payoff balance" as what it says. This is my interpretation because the OP is comparing these two so they must not be the same thing. Therefore I interpret the question to ask "why is my principal barely changing" which might happen if he was making payments against a large sum of accrued interest. – Matt Mar 02 '16 at 16:35
Additionally there is a distinction between interest and principal because payments against interest are tax deductible. – Matt Mar 02 '16 at 16:38
@Matt For all of my loans interest became part of the principal once a month. Which makes "interest only" payments not really possible. I'd pay on the principal every time hopefully the amount i was paying was more then the amount of interest that had accrued and been merged back into the principal since my last payment. – Brad Mar 02 '16 at 17:54
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"Of course, eventually you have to start paying principal" Unless you're a government... then you just keep adding to the principal forever and devalue the currency. :) – reirab Mar 02 '16 at 17:56
Is the ~95% interest figure referring to the grand total that they pay over the lifetime of the loan? The example only shows about 6% for the annual interest. – Panzercrisis Mar 02 '16 at 20:21
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@Panzercrisis It's meant to imply that of any one payment, the allocation of that payment to paying off interest versus paying principal is such. 95% is probably a slight exaggeration for the average person, though for some income-linked repayment plans it's not. I'll clarify that. – Joe Mar 02 '16 at 20:33
@joe - could I suggest redoing the plots so that the vertical axes all have the same scale? That way we can see that the green (principal) has the same area, and it's easier to see that the starting interest part is the same. – Joel Mar 03 '16 at 04:31
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@reirab Or you get a bailout replacing the loan from one entity with the loan from another. – gerrit Mar 03 '16 at 11:35
Amortization is difficult to for a someone to internalize/understand from education. But given a real life personalizing amortization incident (mine was an upside down car loan), and you become an quasi-expert very quickly. I bet the OP is already a pro. – Paulb Mar 03 '16 at 18:11

Why is my student loan balance not going down?

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