One of the most pondered questions in personal finance is whether you should pay off low interest debt quickly or take the extra money and invest it. While the discussion usually revolves around the pros and cons of paying off your mortgage quickly, for this post I’ll focus on another common scenario with which I’m familiar: a new physician and their student loan debt.

Regular readers of this blog know that I am not a fan of debt and that I’m on a mission to pay off my loans by the end of the year. Mathematically, you will come out ahead if you invest rather than pay off low-interest debt quickly. However, I wanted to actually do the math and see how much that difference is. What follows is a little experiment in numbers. I decided to keep the values exact to the decimal point so that the results of the calculations would be as accurate as possible. With that being said, let’s get this party started!

### The Experiment

#### Study Subjects

We’ll take two physicians, Dr. Investor (Dr. I) and Dr. Payoff (Dr. P). They graduate from residency at the age of 35 and have $180,000 in federal student loans. They plan to work for 30 years and retire at the age of 65.

#### The Constants

They both enter the same medical specialty making the same annual salary. We’ll also assume that they each max out their tax-advantaged retirement accounts ever year in the amount of $23,500 (401k at $18,000 and backdoor Roth at $5,500). They both start out with $0 in retirement savings but with no other types of debts or obligations. Also, they were both able to refinance their student loans at 4% over a 20-year repayment plan with a minimum monthly payment of $1,090.76.

#### The Variables

Dr. P wants to be debt free ASAP and decides to pay off his loan in five years by paying $3,314.97 per month. He will then invest that amount every month for the remaining 25 years until retirement. Dr. I decides to take advantage of the lower interest rate by paying the monthly minimum while investing the extra $2,224.21 instead. He will do this for 20 years until the loan is paid off, then he will invest the full $3,314.97 a month for the remaining 10 years and retire at 65. I’ll also look at scenarios where Dr. I pays off his loans over 15-year and 10-year terms.

#### The Assumptions

We’ll assume that Dr. I and Dr. P make no other additional investments and that they each completely stick with their plans. We will also assume investment returns of 7% real and that they both re-invest all dividends and capital gains.

Here’s a summary of what we have so far:

Dr. Investor

20-year payoff plan: investing $2,224.21 monthly for 20 years, then $3,314.97 for the remaining 10 years

15-year payoff plan: investing $1,983.53 monthly for 15 years, then $3,314.97 for the remaining 15 years

10-year payoff plan: investing $1,492.56 monthly for 10 years, then $3,314.97 for the remaining 20 years

Dr. Payoff

Paying off loan aggressively in 5 years, then investing $3,314.97 monthly for the remaining 25 years

### The Results

Here are the results of the calculations given the scenarios noted above:

Dr. Investor comes out ahead in all scenarios with the maximum difference resulting from a 20-year loan payoff plan. The gap narrows as you decrease the length of the loan payoff. These results illustrate the real benefit of time and compound interest. Having a head start on investing by just five years gives Dr. I over $193k more at retirement. Depending on your annual withdrawal rate, this amount could provide another two to three more years of retirement income. The question then becomes whether or not that extra money is worth carrying student loan debt for 15 additional years instead of just paying it off in five. For some people, the answer will be yes… for others, no. But to really answer this question, we need to look at the big picture.

#### The Other Half of the Equation

Let’s now take a step back and factor in all of their retirement savings. As mentioned before, Drs. I and P each contribute the maximum to their 401k’s and Roth IRA’s to the tune of $23,500 annually. Assuming an investment return of 7% real and a 30-year time horizon, they each will have $2,303,123.09 at retirement. Combining this amount with their other investments would give us the following:

#### Dr. Investor

$2,803,446.53 + $2,303,123.09 = $5,106,569.62 at retirement using the 20-year payoff plan

#### Dr. Payoff

$2,610,437.15 + $2,303,123.09 = $4,913,560.24 at retirement, again with a difference of -$193,009.38

Sure you end up with more money if you invest rather than pay off your loan aggressively, but the difference between the two is not that significant. For instance, using a 4% withdrawal rate, Dr. P’s nest egg of $4.9 million would equate to $196,000 per year of retirement income versus $204,000 with Dr. I’s $5.1 million retirement account. That’s a difference of just $8k per year, which is a premium I’m willing to pay in order to be student loan debt free after five years. These amounts don’t factor in taxes, mainly because I’m too lazy to do those calculations as well. But if we were to assume a 25% effective tax rate for Dr. I and Dr. P, they would be left with $153k versus $147k of annual retirement income, respectively.

#### The Race to FIRE

Next, we’ll take a look at the situation where Drs. I and P would want to get FIRE’d up. In this exercise, we’ll include their retirement savings of $23,500 annually (or $1,958.33 monthly) from the get-go and assume that each have a target retirement amount of $2 million.

#### Dr. Investor

Invests $4,182.54 a month ($1,958.33 + $2,224.21) at 7% annual return

Reach FIRE in 232 months (19.33 years)

#### Dr. Payoff

Pays off loans for five years while investing $1,958.33 a month, then invests $5,273.30 thereafter

Would reach FIRE in 238 months (19.83 years)

In the end, Dr. P would work six months longer to reach financial independence but enjoy almost 15 years of being debt free.

### What About You, SRGO?

For our final experiment, let us take a look at my situation and see how the numbers work out. Again, we’ll compare investing with a 20-year payment plan versus a quick payoff strategy. This time around, however, I’ll use my actual loan amount ($300k) and the fact that I will be able to pay off my loans in three years rather than five when performing the calculations. The retirement time-frame will be 30 years using an annual return of 7%. After running the numbers, investing will come out ahead by just $97,931.14. Since there is no way in heck I want to work for 30 years, I figured out how long it would take to reach the goal of $2M. In this scenario, investing will get me there in 9.75 years versus 10.5 years using the aggressive payoff plan. One issue with this, at least for Investing SRGO, is that he would still have another 10 years of student loan payments to make and budget for. On the other hand, Payoff SRGO will be completely debt free.

### Some Things to Consider

Going through this experiment was quite revealing. While investing does come out ahead in terms of the final numbers, the difference is not that significant, particularly if you factor in other retirement savings. The following are some important take-away points to keep in mind.

### For low-interest debt, investing comes out ahead in terms of terminal wealth

You will end up with more money if you invest any extra money instead of using it to pay off debt quicker. That’s just how powerful time and compounding is. The actual amount you end up with will depend on the loan interest rate, the investment time-frame, and your returns. One thing to keep in mind is that these calculations only work out if you stick with your plan and actually invest that extra money every month for the entire investment time-frame. If you’re disciplined financially and are certain you won’t spend that extra money at some point in time, then go ahead and invest away. If not, you might be better off putting that money toward your debt instead. And while it may seem like using extra money to either invest or pay down debt are your only choices, there might be a third option available that suits you better.

### You should still pay off high-interest debt ASAP

This goes without saying, but you should pay off high-interest debt as quickly as you can. An example is credit card debt with interest rates in the mid to high teens. I personally consider anything 6% or above to be high-interest. Another debt that I would pay off quickly would be a new car loan. Although these technically aren’t high interest, with current rates in the 4-5% range, the fact that new cars depreciate at such a rapid rate makes car loans in general a bad idea.

### Pay yourself first

One thing you can do to make the difference between paying off loans and investing less significant would be to simultaneously save for retirement. I’m a big fan of paying yourself first, even if you’re trying to get out of debt. Any little amount you can put away every month adds up over time. And if you’re able to set aside funds from your paycheck before you see it, you will be less likely to miss that money. Over time you’re lifestyle will adjust to the smaller paycheck.

If you’re paying off debt, saving money, and investing, you’re doing it right

You can’t really go wrong with either investing or paying off low-interest debt quickly. Like the featured image above, either choice can be the right one. Both strategies result in an increase in your net worth. I prefer to be free of student loans, regardless of interest rate, as quickly as possible. But at the end of the day, the decision is a personal one.