How do people ever pay off interest-bearing debt??
December 11, 2022 3:11 AM   Subscribe

My cash stuffing rabbithole (see here) led me to the world of debt snowballs and debt avalanches. People's demonstration of the math never seems to take accruing interest into account - when I try to model this for myself, it seems the debt just keeps getting higher and higher both ways. But clearly both methods have worked for people. What am I missing?

Disclaimer: I don't currently have any interest-accruing debt, and I'm also not American if that makes a difference. This is purely for my own curiosity, hence "grab bag".

Using the example in this video, I made up a spreadsheet with the following info:

Personal Loan - $20,000 balance - 15% interest - $400 min payment
Credit Card - $10,000 balance - 10% interest - $200 min payment
Student Loan - $8,000 balance - 5% interest - $100 min payment
Extra: $100

In both cases, every month you pay off everyone's minimum payment, and you apply the extra to whatever choice of loan is your first (in this example: snowball - student loan, avalanche - personal loan). I can see how it works if you are just working with the principal. However, when I tried to account for interest, this is what happens within the first three months:

SNOWBALL
Month One
Student Loan Starting Balance: $8,000
Student Loan Ending Balance: $8,000 - $100 - $100 = $7,800
---
Credit Card Starting Balance: $10,000
Credit Card Ending Balance: $10,000 - $200 = $9,800
---
Personal Loan Starting Balance: $20,000
Personal Loan Ending Balance: $20,000 - $400 = $19,600

Month Two
Student Loan Starting Balance: $7,800 + 5% = $8,190
Student Loan Ending Balance: $8,190 - $100 - $100 = $7,990
---
Credit Card Starting Balance: $9,800 + 10% = $10,780
Credit Card Ending Balance: $10,780 - $200 = $10,580
---
Personal Loan Starting Balance: $19,600 + 15% = $22,540
Personal Loan Ending Balance: $22,540 - $400 = $22,140

Month Three
Student Loan Starting Balance: $7,990 + 5% = $8,389.50
Student Loan Ending Balance: $8,389.50 - $100 - $100 = $8,189.50
---
Credit Card Starting Balance: $10,580 + 10% = $11,638
Credit Card Ending Balance: $11,638 - $200 = $11,438
---
Personal Loan Starting Balance: $22,140 + 15% = $25,461
Personal Loan Ending Balance: $25,461 - $400 = $25,061

AVALANCHE
Personal Loan Starting Balance: $20,000
Personal Loan Ending Balance: $20,000 - $400 - $100 = $19,500
---
Credit Card Starting Balance: $10,000
Credit Card Ending Balance: $10,000 - $200 = $9,800
---
Student Loan Starting Balance: $8,000
Student Loan Ending Balance: $8,000 - $100 = $7,900

Month Two
Personal Loan Starting Balance: $19,500 + 15% = $22,425
Personal Loan Ending Balance: $22,425 - $400 - $100 = $21,925
---
Credit Card Starting Balance: $9,800 + 10% = $10,780
Credit Card Ending Balance: $10,780 - $200 = $10,580
---
Student Loan Starting Balance: $7,900 + 5% = $8,295
Student Loan Ending Balance: $8,295 - $100 = $8,195

Month Three
Personal Loan Starting Balance: $21,925 + 15% = $25,213.75
Personal Loan Ending Balance: $25,213.75 - $400 - $100 = $24,713.75
---
Credit Card Starting Balance: $10,580 + 10% = $11,638
Credit Card Ending Balance: $11,638 - $200 = $11,438
---
Student Loan Starting Balance: $8,195 + 5% = $8,604.75
Student Loan Ending Balance: $8,604.75 - $100 = $8,504.75

and the trendline continues ad infinitum.

Making the extra payment be enough to cover the interest amount for month 2 plus a bit extra (I used $500 for Snowball and $3000 for Avalanche) sorta worked but not fully - it worked on the first Snowball debt and the first 2 Avalanche debts, but both ways the third debt had ballooned out of control and there was no rescuing it even with much more money thrown at it. (The $8,000 student loan turned into over $110,000 over 24 months in Avalanche and the $20,000 personal loan went over $410,000 on Snowball!!)

I've heard people use the term "principal reduction" but from my Googling this only applies to hone loans (Potentially). Are people just paying down the principal and not worrying about the interest at all? Is each month's calculation based on the principal being reduced by the minimum payment? What happens to the interest afterwards?

If it's not principal reduction: do you just make sure your extra payment can cover the interest amount for all the debts? Is there something missing in my math? Some other peculiar thing about debt repayments I don't know about? WRAGH!
posted by creatrixtiara to Grab Bag (13 answers total) 5 users marked this as a favorite
 
Best answer: Interest rates would normally be annual, your sums are treating them as monthly.
posted by gregjones at 3:23 AM on December 11, 2022 [25 favorites]


Best answer: Seconding that your interest rate math is wrong (again, assuming annual interest rates, which is typical):

Month Two for your student loan example would be:
Student Loan Starting Balance: $7,800 + 5%/12 = $7,832.50
Student Loan Ending Balance: $7,832.50 - $100 - $100 = $7,632.50

Your math shows why usury caps are important! A 5% monthly rate would be a 60% annual rate, which is much, much harder to pay off.
posted by snaw at 3:47 AM on December 11, 2022 [6 favorites]


Response by poster: Interest rates would normally be annual, your sums are treating them as monthly.

ooooooohhhhhhhh

I think I got so used to the "you got 1 cent in interest this month!" messages from my bank account that I assumed it applied the other way, whoops

thank you!!!
posted by creatrixtiara at 4:01 AM on December 11, 2022 [4 favorites]


As an addition, usually the minimum payments are set by the lender so that they at least cover the interest. On personal loans, they are typically set so that you will repay the whole loan by the end of the term. Credit cards and student loans can differ. But for the debt snowball/avalanche system to work, the amount you pay towards each loan must be at least as high of the interest, basically you're preventing those from getting any worse while you tackle the first one. Otherwise, what happens is what you're seeing, that the balance just gets away from you.

JD Roth (of Metafilter) paid off his debt using this approach and chronicled it on his excellent personal finance blog. Others have done the same.
posted by plonkee at 5:25 AM on December 11, 2022 [7 favorites]


Depending on various factors, interest rates can also vary widely. Many U.S.-ians pursue various tactics to shift credit card balances from lender to lender to take advantage of 6-12-month windows of very low interest. This is something many people do, but it often goes double for folks working on debt intensively.
posted by cupcakeninja at 5:51 AM on December 11, 2022 [1 favorite]


I think I got so used to the "you got 1 cent in interest this month!" messages from my bank account that I assumed it applied the other way, whoops

Well, it does. The interest rate quoted for a savings account would also be the annual rate, but it's earnt more frequently - often calculated daily but paid to you monthly.
posted by gregjones at 6:09 AM on December 11, 2022 [2 favorites]


Your math shows why usury caps are important! A 5% monthly rate would be a 60% annual rate, which is much, much harder to pay off.

A recent question or r/personalfinance illustrates this perfectly: "Took out a personal loan for $450 and the expected cost is over $2000. Is this normal?"

Someone in the comments calculated that their loan terms work out to around 688.55% APR. With the low payments, it is basically what you calculated in your spreadsheet -- the person can barely get in front of it and even then there is a huge cost. Lowering the payments, or missing a few, will create even higher total costs and potentially letting the debt spiral up.

Paying off "regular" credit is hard enough; paying off predatory credit is near-impossible.
posted by Dip Flash at 6:36 AM on December 11, 2022 [5 favorites]


There are often legal limits on the rate of interest. It looks as though in the USA it's a rather complicated patchwork of state rules that may sometimes be bypassed with customer consent, while in Canada it's a federal criminal offence to charge or receive interest over an effective annual rate of 60% of the cost of the loan (i.e. including monthly compounding if applicable), though with some legislated exemptions for small value and short term payday loans.
posted by lookoutbelow at 7:56 AM on December 11, 2022 [1 favorite]


Best answer: As above - for interest there's a RATE (almost always quoted as an annual percentage rate or APR) and a COMPOUNDING PERIOD (could be any time duration). You should divide the RATE by the number of COMPOUNDING PERIODS in a year whenever you use it to calculate how much interest you'll pay.

So if you have 12% interest compounded yearly, at the end of each year you owe 12% more.
If it's compounded monthly, at the end of each month you owe 1% more (12% / 12).
If it's compounded daily, at the end of each day you owe .0328% more (12% / 365).

The more frequent the compounding period the (slightly) more you pay overall, because you end up paying interest on interest you've already accrued.

A simple calculator you can play around with can be found here
posted by true at 8:02 AM on December 11, 2022 [6 favorites]


If you are in income-based repayment for your student loans, then it is quite common for the loan balance to grow and grow. In theory you will then be able to get the balance forgiven in time, but that is one other potential complication to your math as well.
posted by rockindata at 8:44 AM on December 11, 2022


As others have pointed out, you were treating the stated interest rate as a monthly rate, not an annual rate.

In the United States, in almost every circumstance, bank interest rates are required by law to be quoted as an annual percentage rate, regardless of the other terms of the loan.

If I'm a bank, it would be perfectly legal for me to loan you money and accrue the interest at 0.301% every week. But it would be illegal for me to describe it - in documents or in advertisements - as anything but a 17% APR.

(1.00301 ^ 52.14 ~= 17%)
posted by Hatashran at 9:08 AM on December 11, 2022


How do people ever pay off interest-bearing debt??

Math errors aside, there is an awful lot of predatory lending in the US, so sometimes the answer is that they don't. payday loans are one of the most egregious ones I know, and if you calculate the fees as APR (since they amount to the interest, especially if you can't repay immediately) they can be well in the hundreds of percent range. They are essentially designed for the trap you are wondering about, targeting people in very low income ranges. From that last link: "The average borrower takes out 10 loans and pays 391% in interest and fees. 75% of the payday industry’s revenues are generated by these repeat borrowers. The debt trap is, in fact, the payday lending business model."
posted by advil at 9:41 AM on December 11, 2022 [2 favorites]


Others have addressed your math misconception and the problems of predatory lending, but the reason to do a debt snowball is psychological. Some people are encouraged by the smaller, more attainable wins of fully paying off debt along the way, even if that means they are not paying off their total debt at the highest rate they could. (For those with truly fragile finances, it also gives you a little more flexibility in emergencies if your two minimum payments of $30/mo. to A and B go down to one to A. Of course, if you don't apply the B money to increasing the A payment to $60, you're slowing the rate of savings, but if it's a choice between slowing the rate of savings and making payments late or going into default, it's an easy choice.)

This approach doesn't work for me, but I will say that its advocacy represented one of the first breakthroughs in popular personal finance of the true concept that debt management involves psychology as well as math. For many people, the total extra interest paid is relatively small. Of course, if you have a 1000-point spread between rates, as in your example, the difference between the two approaches can be substantial, but a lot of people mostly have credit cards within a relatively narrow of interest rates.
posted by praemunire at 10:15 AM on December 11, 2022


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