In the interest of full disclosure, I want to acknowledge my bias against taking early distributions from 401(k) and similar accounts. I feel this way for two reasons. First, there is a 10% penalty tax for taking a distribution before age 59½. Second, the money in pre-tax retirement accounts was set aside for, well, retirement. You may have other options for handling the debt that avoids depleting an account designed to support you when you stop working.
You have several other concerns, including a) overall cost vs. monthly expense, and b) present vs. future value of money. Let us explore these issues.
Overall Cost vs. Monthly Expense
My guess is your monthly student loan payment is $250 per month. Let us assume you take a $20,000 distribution from your retirement account. Let us assume you are less than age 59½. You will pay a 10% penalty tax off of the top, which will leave you $18,000. Because 401(k) funds are pre-tax, you will also need to pay your regular income tax rate on that $18,000, which will vary by your circumstances. Let us assume for the sake of argument that you are in the 20% tax rate. This means your $20,000 distribution will net you $14,400 after federal taxes.
If you apply the $14,400 to the loan and continue to pay $250 per month, you will have cut the time to debt freedom by more than half. However, you will have severely depleted your 401(k). In response to this, you will need to ratchet-up your contribution to the maximum allowed by your employer, which will probably be 12%. When you achieve debt freedom, you will need to maximize your contribution to IRA and Roth IRA accounts to catch-up to what you lost when you took a distribution from your 401(k).
My point is that taking a 401(k) distribution my result in lower interest costs, but will almost certainly result in the increased monthly expense of saving for your retirement.
Present v. Future Value
I will assume your math is accurate regarding the interest cost of the loan over 20 years. Let me add one caveat to your analysis. As I write these words in mid-2010, the inflation rate has varied from zero to about 3.5% over the last 10 years. I am not a follower of financial apocalypticism. However, given the recent spending rate of the US government I believe it likely the inflation rate will increase over the next few years.
One benefit to debtors in times of inflation is they repay loans with dollars that are worth less than when they received the loan. Let me put this in concrete terms. Let us say that the US inflation rate stays a constant 3% over the next 20 years. A $10 bill today will have the same purchasing power as $18 in 20 years. If inflation averages 3.5%, a $20 bill in 20 years will have the same purchasing power as a $10 bill today. If the interest rate on your loan is fixed, then as you repay the loan you hand over the the same number of dollar bills you did on day one, but with each passing month each dollar bill you pay is worth less. Therefore, if you believe the inflation rate will stay low, then you will be inclined to repay the loan quickly. However, if you believe the inflation rate will increase, then it is smarter to repay the loan later when dollars will be worth less. High inflation, in effect, slashes the interest rate on a fixed-rate loan.
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Let us assume monthly cash-flow is not an issue for you. One option is to borrow $26,000 from your 401(k) to retire the student loan. The advantage of a 401(k) loan is that you do not pay the 10% penalty tax. You also avoid income tax. The interest rate that you pay on the 401(k) loan is paid to your account — in other words, you. When the loan is repaid you have replenished your 401(k), which is an excellent outcome.
The downside to a 401(k) loan is that if you fail to make your loan payments your 401(k) administrator is required to treat the loan as a distribution, and you will pay the 10% penalty tax plus your usual tax rate. It is in your best interest to repay your 401(k) loan.
I hope this information helps you Find. Learn & Save.