Thursday, October 25, 2012

The Thing That Couldn’t Die, Part 2: Why Pay Off Debt? (The Math)

Photo courtesy of

Warning:  I am not a math nerd. I used Excel to help me calculate the figures below, and I compounded the interest monthly, rather than daily, so the calculations are approximate.  

I was recently involved in an internet discussion regarding paying down debt quickly.  I talked a little about my experience delivering pizza, and someone interjected with this argument:

Hey, I'm really really not being a jerk here okay?
But I just want to interject something. When I was finishing my private school in law (I went to two schools, the first one I hated, the second was more expensive but it was so much better), we had a lecture on the "practical side of life." What came out in this lecture was that since student loans were so low on interest it was at times better to invest your money than pay down your loans.

Again, not being a jerk just putting that out there. I attempted to pay off my loans also, but got sidetracked by the recession. Also I'm really into finance (shouldn't have gone to law school at all but it's been done) and I actually became a day trader instead.
I wouldn't question your choices, but definitely wanted to make sure you had considered this. Student loans are usually government backed loans, so it’s not risk to invest your money at a better interest rate than your loan--usually. Did you know that under the terms of President Obama's “Student Loan Forgiveness Act 2012,” that if you pay consistently never missing a payment for 10 years, that your loan will be forgiven? Also, under the Act the payment is calculated at a VERY very low percentage of your income and will always be tied to a percentage of your income no matter how big or small it is? In factuality, I went from paying about $300 to $50 a month. But that's not all! The people reorganizing my loan offered to let me pay at $25/mo.!!!! WTF, right?! This is a totally true factual story. That law is meant to help you and everyone else get back on their feet after the recession and out from under these crushing loans.
What you guys are doing is awesome, but if you've paid down half your debt already, you might want to have a pow-wow and see if these are still your most desired goals!! Peace.
This got me to thinking about some debt myths, particularly regarding student loans.  First, let’s clear up some misconceptions that this person has about student loan forgiveness.  As I pointed out:

There is no student loan forgiveness law that will just forgive your loans if you make ten years of payments. There is an act called The College Cost Reduction and Access Act of 2007 (which of course was enacted before Obama became President), which will forgive loans after 120 payments to the Direct Loan program. BUT - this is only for those who work in public service (government jobs mostly), and you must be employed full-time in public service for those ten years. Most borrowers will not qualify for this program.
There is another provision of the same act that will forgive loans after 25 years, but “[i]ncome-based repayment is only available for federal student loans, such as the Stafford, Grad PLUS and consolidation loans. It is not available for Parent PLUS loans or for consolidation loans that include Parent PLUS loans.”
Also, any portion of the loan that is forgiven after 25 years is treated as taxable income.
Finally, please note that these programs are only for certain federal loans. Private borrowers cannot avail themselves of these laws.
I think the upshot of this discussion is that there are a couple of ways student debt can be forgiven: if you are lucky enough to be employed by the government for 10 years straight, and making on-time payments during that time, or if you are willing to wait around for 25 years, paying less than the monthly interest, and then paying taxes on the forgiven balance.  Here’s why I’m not doing that.  In this post, I’m only going to discuss the math.  In my next post, I’ll discuss the psychology.

1.      I have the ability to repay my loans, and I do not work for the government.  Since I
am not going to benefit from an income-based repayment plan, or from public service loan forgiveness, I am not going to have any portion of my balance forgiven in 25 years or in 10 (unless something catastrophic were to happen). 

2.     There is no substantial mathematical benefit to relying on loan forgiveness in 25
years.  Let’s suppose I wanted to hedge my bets and make the minimum payment in case something terrible does happen.  Mathematically, I would not substantially benefit.  Here’s why: 

If I luck out (like the above-poster thinks he did) and only have to pay $50 per month for the next 20 years (I’ve already been paying for about 5, so that would be the remaining term of my federal loans)., that means I’ll be paying $600 per year, or $12,000 over 20 years.  This does not even begin to keep up with the interest (the average of my subsidized and unsubsidized loans is 3%), which means when all is said and done, in 20 years, I will still owe $111,037.75. 

That will count as income at the time it is forgiven.  Let’s assume I make no other income that year, and let’s also assume current tax rates.  That puts us in the 25% federal tax bracket.  This means I owe federal income tax of $27,759.44.  I would also owe 9.3% for state income taxes, which comes to $10,326.51.  In total, I will have spent $50,085.95 (not to mention the 5 years of payments I’ve already made, but I won’t even count those) in repaying my loans.  So, in order to save less than $20,000, I will have accrued additional interest that inflates my balance well past six figures.  And I now owe $38.085.95 to the IRS and to the state.  I am pretty sure I am not going to be able to pay this off in a lump sum, since my financial straits qualified me for such a low payment schedule to begin with. 

So, I am still in debt to the federal government, right?  Only this time I owe the IRS, which has a bit of a reputation for aggressive collection tactics.

And let’s not forget that I am relying heavily on the assumption that the federal government is going to forgive my debt in 20 years, which might not be true.  A lot can happen between now and 2032.

To me, it doesn’t make mathematical sense to save less than $20K over a 25 year period, only to end up in debt to the IRS. 

But let’s address the other argument, that you can make a better rate of return by simply investing your extra money, rather than paying off debt first.  

3.  It is a myth that you will make more by paying only the minimums and investing discretionary income elsewhere.  Let’s say it takes me 3 years to pay off my student loans, as well as all my other debt, starting a year and a half ago (our goal is still to pay it off sooner, but let’s assume the original goal).  Let’s do the math on how much interest was saved:
Loan Type
Interest Under Standard Repayment
Interest Under Accelerated Repayment
Auto Loan (5.5%)
$ 3,303.22
$ 1,414.22
Private SL 1 (5%)
$  5,000
$    869.75
$    624.77
Private SL 2 (7.9%)
$ 4,546.65
$ 2,460.67
Federal SL 1 (5%)
$ 5,603.20
Federal SL 2 (3%)
Total Int. Paid


Total Interest Savings Under Accelerated Payment Plan: $25,768.05

Now, let’s suppose I put all of my extra money into debt repayment for 3 years, and then
start investing once I am debt-free.  All of the fixed payments each month total $1,192.02.  So that amount will become discretionary once I am debt-free.  On top of that, I have the extra money I was throwing toward the debt snowball each month, which averaged out to be $3,727 each month.  So that means I will have $4,919 to invest each month once I am no longer paying back debt. 

Let’s say I put that amount into an investment with a 5% annual rate of return.  $59,028 per year for 30 years = $4,176,867.50.

Now let’s say I keep my debt and put $3,727 into an investment with a 5% annual rate of return for 33 years.  $44,724 per year for 33 years = $3,804,534.50.

By paying off debt early, you’ve made $372,333.

Stay tuned for my thoughts on the psychological benefits of paying off debt quickly…


  1. Wow, great blog.Really looking forward to read more. Really Cool.
    Optometry practice financing

  2. Thanks for sharing, this is a fantastic post.Thanks Again. Fantastic.
    best suits for men