401(k) or student loan (more importantly: a math question)
401(k) or student loan (more importantly: a math question)
Hi all,
I recently discovered both this site and the Bogle theory on index fund investment. I am just now taking my retirement finance management seriously. I will be getting married in the near future and it has had a sobering effect on my life goals. (Not that I was ignoring my future; I do have a considerable bit of retirement savings that I managed to build up before grad school.) I have learned a lot from the postings here and I am looking forward to learning more. Based on what I have found searching this forum, I think my question is a nobrainer but, as my SO would say, I need to be validated. Additionally, I have been searching for math that will make my understanding of the Boglehead viewpoint on paying down debt vs. investing crystal clear  or approximately so.
Facts:
 Income tax bracket: ~31% + ~9% = 40% (This assumes no 2013 tax cut extension and CA income tax.)
 student loan debt ~200k
 component of student loan debt @8.5% interest ~43k (BTW, I will be telling my kids not to go to private schools if they can help it)
 the rest of my student loan debt is < 6.9% (and given the large 8.5% component, the rest of my loans are inconsequential to my immediate dilemma)
 emergency fund: ~6k (approx 6 months of expenses)
 my employer has a 401(k) starting Jan. 1 2013, no match
 I have another ~ 25 years before I am required to start my 401(k) withdrawals.
Question: Should I pay down my 8.5% debt or invest in 401(k) or some mix?
My answer based on what I have read on the forums: Pay down the damn debt. (Am I wrong here?)
Math Question: How can I relate my 8.5% debt to a pretax 401(k) investment so that I can compare numbers?
 the 8.5% debt is, worst case, 25 years in repayment. Compounding can be avoided if I do my paperwork right...I think.
 I understand that I can translate debt repayment into a bond equivalent for math purposes.
 I still don't understand how to compare this to a similar pretax (40% savings in my case) equivalent investment, assuming the 25 year worstcase scenario (and I can't figure out intermediate scenarios either). I am interested in understanding the comparison of the debt to riskaverse investment alternatives in:
1) the short term; and
2) the long term (i.e. once I need to withdraw, taxes will impact this)
I realize that (2) requires me to make some assumptions about the future. So, I am approaching it as 'all things being equal years from now' (probably not accurate; corrections welcome)
I also realize that 8.5% guaranteed is unheard of. My concern is with the impact of the use of pretax dollars.
Ultimately, I think I know the answer to my practical question. The issue I am having is understanding the math that gets me to that point.
I would love to hear any thoughts on either portion of this.
(A sidenote: I am so happy to finally find a forums that deals in unhyped objective longterm goals. I just bought my brother a Bogleheads book for Christmas.)
Thanks in advance for any feedback
I recently discovered both this site and the Bogle theory on index fund investment. I am just now taking my retirement finance management seriously. I will be getting married in the near future and it has had a sobering effect on my life goals. (Not that I was ignoring my future; I do have a considerable bit of retirement savings that I managed to build up before grad school.) I have learned a lot from the postings here and I am looking forward to learning more. Based on what I have found searching this forum, I think my question is a nobrainer but, as my SO would say, I need to be validated. Additionally, I have been searching for math that will make my understanding of the Boglehead viewpoint on paying down debt vs. investing crystal clear  or approximately so.
Facts:
 Income tax bracket: ~31% + ~9% = 40% (This assumes no 2013 tax cut extension and CA income tax.)
 student loan debt ~200k
 component of student loan debt @8.5% interest ~43k (BTW, I will be telling my kids not to go to private schools if they can help it)
 the rest of my student loan debt is < 6.9% (and given the large 8.5% component, the rest of my loans are inconsequential to my immediate dilemma)
 emergency fund: ~6k (approx 6 months of expenses)
 my employer has a 401(k) starting Jan. 1 2013, no match
 I have another ~ 25 years before I am required to start my 401(k) withdrawals.
Question: Should I pay down my 8.5% debt or invest in 401(k) or some mix?
My answer based on what I have read on the forums: Pay down the damn debt. (Am I wrong here?)
Math Question: How can I relate my 8.5% debt to a pretax 401(k) investment so that I can compare numbers?
 the 8.5% debt is, worst case, 25 years in repayment. Compounding can be avoided if I do my paperwork right...I think.
 I understand that I can translate debt repayment into a bond equivalent for math purposes.
 I still don't understand how to compare this to a similar pretax (40% savings in my case) equivalent investment, assuming the 25 year worstcase scenario (and I can't figure out intermediate scenarios either). I am interested in understanding the comparison of the debt to riskaverse investment alternatives in:
1) the short term; and
2) the long term (i.e. once I need to withdraw, taxes will impact this)
I realize that (2) requires me to make some assumptions about the future. So, I am approaching it as 'all things being equal years from now' (probably not accurate; corrections welcome)
I also realize that 8.5% guaranteed is unheard of. My concern is with the impact of the use of pretax dollars.
Ultimately, I think I know the answer to my practical question. The issue I am having is understanding the math that gets me to that point.
I would love to hear any thoughts on either portion of this.
(A sidenote: I am so happy to finally find a forums that deals in unhyped objective longterm goals. I just bought my brother a Bogleheads book for Christmas.)
Thanks in advance for any feedback
Re: 401(k) or student loan (more importantly: a math questio
Hi Ron,
I'm just heading out to lunch so can't run too many numbers but here are my initial thoughts:
1. With your nasty taxbracket, the aftertax rate on your 8.5% student loan is only 5.1%, assuming that the interest is deductible from CA income taxes?
2. The 401k is appealing since you may be in a much low tax rate in the future BUT 5.1% is a much better rate than you'd get on any sort of investment that's even close to as reliable as a student loan; as sure as you're going to die, you're going to pay off that student loan. In other words, from an alternative investment comparison, the 401k can't compete.
3. Do you have any equity in your house to could leverage to get rid of the $43k, higherinterest component?
4. You'd be wise to go be a rural doctor or something to get those loans forgiven
Good luck!
I'm just heading out to lunch so can't run too many numbers but here are my initial thoughts:
1. With your nasty taxbracket, the aftertax rate on your 8.5% student loan is only 5.1%, assuming that the interest is deductible from CA income taxes?
2. The 401k is appealing since you may be in a much low tax rate in the future BUT 5.1% is a much better rate than you'd get on any sort of investment that's even close to as reliable as a student loan; as sure as you're going to die, you're going to pay off that student loan. In other words, from an alternative investment comparison, the 401k can't compete.
3. Do you have any equity in your house to could leverage to get rid of the $43k, higherinterest component?
4. You'd be wise to go be a rural doctor or something to get those loans forgiven
Good luck!
 market timer
 Posts: 5528
 Joined: Tue Aug 21, 2007 1:42 am
Re: 401(k) or student loan (more importantly: a math questio
Answer depends on how much you save per year and what your expected tax rate on withdrawals will be. Someone who will be able to withdraw taxfree from the 401K and who can expect to pay off the 8.5% interest loans in the next several years should max out the 401K. Someone else who doesn't save enough to max out the 401K in a typical year should probably just focus on debt repayment. One way around this dilemma is to max out the 401K and then take a 401K loan to pay down your loans. Then you get your tax deduction without slowing down student loan repayment.
Re: 401(k) or student loan (more importantly: a math questio
brianbooth wrote:Hi Ron,
I'm just heading out to lunch so can't run too many numbers but here are my initial thoughts:
1. With your nasty taxbracket, the aftertax rate on your 8.5% student loan is only 5.1%, assuming that the interest is deductible from CA income taxes?
This is incorrect as the max amount you can deduct is $2500. Plus your MAGI has to be lower than $75000 or thereabouts, so OP might make too much money to deduct even that.
Re: 401(k) or student loan (more importantly: a math questio
A couple of other issues to think about (just some random thoughts I have when I ponder the same question):
1. Student loans generally die with you, but funds in retirement accounts can be passed on to a surviving spouse, heir, etc.
2. Student loans are hard to get rid of (can't discharge in bankruptcy), but 401k funds are also afforded a ton of protection in bankruptcy and against judgments in lawsuits and such.
3. Student loan forgiveness options  Income based repayment, PSLF, etc.
1. Student loans generally die with you, but funds in retirement accounts can be passed on to a surviving spouse, heir, etc.
2. Student loans are hard to get rid of (can't discharge in bankruptcy), but 401k funds are also afforded a ton of protection in bankruptcy and against judgments in lawsuits and such.
3. Student loan forgiveness options  Income based repayment, PSLF, etc.
Re: 401(k) or student loan (more importantly: a math questio
The math here doesn't seem too difficult if you assume your tax rate now is the same as your tax rate later. (It seems quite similar to the question of whether to use a roth 401k). Suppose you have $100 of income and you want to decide whether to put it in your 401k or use it to pay off your loans.
Scenario #1: You contribute $100 to your 401k. It grows at a rate of R% for N years, and then you pay 40% taxes on it: 100 * (1+R)^N * .60
Scenario #2: You pay taxes on your $100. This gets you 8.5% a year for N years: 100 * .60 * 1.085^N
Just like a Roth vs regular 401k, if your tax rate is the same at retirement as it is now then it doesn't make a difference if you pay taxes now or later. Taking the "guaranteed" 8.5% return from paying off the loan seems like a big win (sounds like you've already come to this conclusion!).
Scenario #1: You contribute $100 to your 401k. It grows at a rate of R% for N years, and then you pay 40% taxes on it: 100 * (1+R)^N * .60
Scenario #2: You pay taxes on your $100. This gets you 8.5% a year for N years: 100 * .60 * 1.085^N
Just like a Roth vs regular 401k, if your tax rate is the same at retirement as it is now then it doesn't make a difference if you pay taxes now or later. Taking the "guaranteed" 8.5% return from paying off the loan seems like a big win (sounds like you've already come to this conclusion!).

 Posts: 7091
 Joined: Sun Nov 15, 2009 9:24 am
Re: 401(k) or student loan (more importantly: a math questio
Seriously. The good news is that the interest on the first $37,000 of your $200,000 of debt would be deductible if you weren't way, way over the income limit and if the student loan interest deduction as such weren't expiring in eleven days.countofmc wrote:This is incorrect as the max amount you can deduct is $2500. Plus your MAGI has to be lower than $75000 or thereabouts, so OP might make too much money to deduct even that.brianbooth wrote:Hi Ron,
I'm just heading out to lunch so can't run too many numbers but here are my initial thoughts:
1. With your nasty taxbracket, the aftertax rate on your 8.5% student loan is only 5.1%, assuming that the interest is deductible from CA income taxes?
Re: 401(k) or student loan (more importantly: a math questio
I see you are in a pretty high tax bracket and your monthly expenses are low. I would max 401K/Roth IRA and put extra cash flow on loans. Increase emergency fund to ~2 years. Should be easy with your income and expenses. Then borrow from 401K to pay off a chunk of loans. Treat 401K loan like a bond. This also increases tax deferred space since interest is paid directly to you. Once you miss a year of tax deferred space you never get it back.
Also, do remember, you deduct 401K contributions at your marginal rate, but upon withdrawal, you fill up lower tax brackets first, making the average rate much lower. This is one of the greatest tax arbitrage opportunities few understand very well outside this website.
grap
Also, do remember, you deduct 401K contributions at your marginal rate, but upon withdrawal, you fill up lower tax brackets first, making the average rate much lower. This is one of the greatest tax arbitrage opportunities few understand very well outside this website.
grap
If you can't explain it simply, you don't understand it well enough.
Re: 401(k) or student loan (more importantly: a math questio
grap0013 wrote:Also, do remember, you deduct 401K contributions at your marginal rate, but upon withdrawal, you fill up lower tax brackets first, making the average rate much lower. This is one of the greatest tax arbitrage opportunities few understand very well outside this website.
grap
The finance buff has a good demonstration of this in his "Case Against a Roth" article: http://thefinancebuff.com/caseagainstroth401k.html I think a lot of that applies here. Still, it's a gamble based on the future tax rates. The OP stated that the 31% is under the assumption that the tax cuts expire, and given that the OP is presumably young and newly hired, it's entirely possible that the tax rate will be higher later on. Paying off the loan is a sure thing, while the 401k return is not.
Re: 401(k) or student loan (more importantly: a math questio
Your monthly expenses are only $1k? You list a $6k EF that covers 6 months. Something is off here. Not sure it matters in the end.
 Bill
Re: 401(k) or student loan (more importantly: a math questio
I would pay off the debt. There is significant psychological benefits to doing so
Re: 401(k) or student loan (more importantly: a math questio
DTSC wrote:I would pay off the debt. There is significant psychological benefits to doing so
There are a lot of psychological benefits to seeing your networth go up too! I just ignore the "debt" balance in Mint and look at networth.
If you can't explain it simply, you don't understand it well enough.
Re: 401(k) or student loan (more importantly: a math questio
market timer wrote:Answer depends on how much you save per year and what your expected tax rate on withdrawals will be. Someone who will be able to withdraw taxfree from the 401K and who can expect to pay off the 8.5% interest loans in the next several years should max out the 401K. Someone else who doesn't save enough to max out the 401K in a typical year should probably just focus on debt repayment. One way around this dilemma is to max out the 401K and then take a 401K loan to pay down your loans. Then you get your tax deduction without slowing down student loan repayment.
+1.
Do you have a car with any equity? You can borrow against your car for under 2% for five years at PenFed. Use it to pay down the debt.
Re: 401(k) or student loan (more importantly: a math questio
ronima wrote:Math Question: How can I relate my 8.5% debt to a pretax 401(k) investment so that I can compare numbers?
 the 8.5% debt is, worst case, 25 years in repayment. Compounding can be avoided if I do my paperwork right...I think.
 I understand that I can translate debt repayment into a bond equivalent for math purposes.
 I still don't understand how to compare this to a similar pretax (40% savings in my case) equivalent investment, assuming the 25 year worstcase scenario (and I can't figure out intermediate scenarios either).
Adjust the return for the difference in tax rates. If you retire in a 40% tax bracket, and will withdraw the money 30 years later in a 30% tax bracket, then it costs you $6000 to put $10,000 in the 401(k), and you will get the future value of $7000 out. This is a 17% gain, or 0.52% annualized; thus, if you invest the 401(k) in bonds earning 3%, you will earn 3.52%.
There is one additional issue: if you don't max out your 401(k) now, then you may have to make taxable investments later, and thus you will lose the benefit of some of the tax deferral. However, with a rate as high as 8.5%, the benefit of tax deferral isn't worth the difference.
 market timer
 Posts: 5528
 Joined: Tue Aug 21, 2007 1:42 am
Re: 401(k) or student loan (more importantly: a math questio
grabiner wrote:This is a 17% gain, or 0.52% annualized; thus, if you invest the 401(k) in bonds earning 3%, you will earn 3.52%.
There is one additional issue: if you don't max out your 401(k) now, then you may have to make taxable investments later, and thus you will lose the benefit of some of the tax deferral. However, with a rate as high as 8.5%, the benefit of tax deferral isn't worth the difference.
You should annualize the 17% benefit over the duration of student loan repayment. That is, if someone is paying 8% abovemarket (say, spread to shortterm treasuries) for only a year, it is worth bearing this cost to get a 17% benefit. If it will take 10 years to pay down the student loan, the comparison is less favorable. That's why savings rate matters. It's also worth considering the value of tax deferred compounding, not just difference between contribution and withdrawal marginal tax rates. Having access to a 401K loan further improves the comparison.
Re: 401(k) or student loan (more importantly: a math questio
grap0013 wrote:I see you are in a pretty high tax bracket and your monthly expenses are low. I would max 401K/Roth IRA and put extra cash flow on loans. Increase emergency fund to ~2 years. Should be easy with your income and expenses. Then borrow from 401K to pay off a chunk of loans. Treat 401K loan like a bond. This also increases tax deferred space since interest is paid directly to you. Once you miss a year of tax deferred space you never get it back.
Also, do remember, you deduct 401K contributions at your marginal rate, but upon withdrawal, you fill up lower tax brackets first, making the average rate much lower. This is one of the greatest tax arbitrage opportunities few understand very well outside this website.
grap
+1 to what he said.
I'm assuming from your tax bracke you have a very healthy salary and it seems like you still have a very low cost (relative to your salary) lifestyle. I would prioritize the following way:
1. Max 401k
2. Max Backdoor Roth IRA
3. Throw everything you can muster at your debt starting with the highest interest rates first
My big question is if you did this, how much could you be paying off each year? If you make around or above 200k I think you could realisticly throw 34 per month at this and be done in 56 years.
Re: 401(k) or student loan (more importantly: a math questio
grabiner wrote:ronima wrote:Math Question: How can I relate my 8.5% debt to a pretax 401(k) investment so that I can compare numbers?
 the 8.5% debt is, worst case, 25 years in repayment. Compounding can be avoided if I do my paperwork right...I think.
 I understand that I can translate debt repayment into a bond equivalent for math purposes.
 I still don't understand how to compare this to a similar pretax (40% savings in my case) equivalent investment, assuming the 25 year worstcase scenario (and I can't figure out intermediate scenarios either).
Adjust the return for the difference in tax rates. If you retire in a 40% tax bracket, and will withdraw the money 30 years later in a 30% tax bracket, then it costs you $6000 to put $10,000 in the 401(k), and you will get the future value of $7000 out. This is a 17% gain, or 0.52% annualized; thus, if you invest the 401(k) in bonds earning 3%, you will earn 3.52%.
There is one additional issue: if you don't max out your 401(k) now, then you may have to make taxable investments later, and thus you will lose the benefit of some of the tax deferral. However, with a rate as high as 8.5%, the benefit of tax deferral isn't worth the difference.
Just to piggyback onto this with two examples using 2012 tax info.
Example #1:
MFJ earning 100K.
401K contributions are deducted from 25% marginal rate.
For 100K income in retirement you will pay $12,185 in federal taxes or an average rate of 12.2%. So it's 25% vs. 12.2%
Exampled #2:
MFJ earning 250K
401K contributions are deducted from 33% marginal rate.
For 250K income in retirement you will pay $52,971 in federal taxes or an average rate of 21.1%. So it's 33% vs. 21.1%
Looks like the "spread" hovers around 12% using a couple basic examples. I haven't even mentioned state income taxes which further supports maxing tax deferred space as highest priority. If the OP retires in Florida...
If you can't explain it simply, you don't understand it well enough.