Reader Dan left this comment on my post last week about paying a 30-year loan on a 15-year schedule:

Having your house paid off in 15 years instead of 30 will provide peace of mind in 15 years. But at what cost?

The opportunity cost of locking that money up in the equity of your house could be significant if you invest the difference.

According to Bankrate.com, the Annual effective interest rate for a 4% mortgage, after taxes are taken into account is 2.76%.

Reader Heidi also asked:

Although it would be nice to sell the house at that time and have no mortgage, I struggle with tying up the funds in a paid off mortgage. My retirement accounts are maxed out, but my taxable investment account could use some additional funds (hopefully earning a higher rate than what I’d pay on the mortgage). Your view?

Many think that because mortgage rates are at historical lows, it’s cheap money, therefore it would be smart to stretch the repayments and invest the difference. To borrow a phrase from buying life insurance — “buy term and invest the difference” — I call this strategy “**borrow 30-year and invest the difference**.”

Let’s run the numbers and see if it’s a good move.

**Example**: Bob refinances a $400k mortgage in California. He can get a 30-year fixed rate mortgage at 3.5% or he can get a 15-year fixed rate mortgage at 2.875% at comparable closing costs. The 30-year mortgage requires a payment of $1,796 per month. The 15-year mortgage requires a payment of $2,738 per month.

Bob decides to take the 30-year mortgage and invest the difference of $942 per month in a “side fund.” Because Bob pays more interest on the 30-year mortgage, Bob gets more tax deductions. Bob also invests the tax savings into the side fund. When Bob finally sells his house, he liquidates the side fund, pays the capital gains tax, and uses the proceeds to pay against the mortgage.

We assume Bob earns 5% on his side fund. For simplicity’s sake, we assume the side fund is perfectly tax efficient. All gains will be long-term capital gains at the time of sale.

We want to compare the increase to Bob’s net worth. That is (a) the principal paid off if Bob took a 15-year mortgage versus (b) the principal paid off on the 30-year mortgage plus the money in the side fund after paying capital gains tax. Whichever strategy results in a larger number wins.

I have detailed calculations in a spreadsheet. You can double-check my math or enter different assumptions. I summarize the net worth increases here:

Year | (A) 15-year | (B) 30-year plus side fund | (B) – (A) |
---|---|---|---|

1 | $21,644 | $19,987 | -$1,657 |

3 | $66,841 | $62,539 | -$4,302 |

5 | $114,711 | $108,803 | -$5,908 |

10 | $247,133 | $243,128 | -$4,005 |

15 | $400,000 | $409,556 | +$9,556 |

At the end of 1, 3, 5, and 10 years, the “borrow 30-year and invest the difference” strategy is worse off than just taking out a 15-year mortgage. Only at the end of 15 years does the side fund finally build up enough to overcome the higher loan balance.

**What’s going on?** How come borrowing tax deductible money at 3.5% to invest at 5% return with perfect tax efficiency and favorable long-term capital gains treatment doesn’t pay off for 12 years?

The answer lies in the **higher rate** on the 30-year mortgage. Although a 0.625% difference between the 15-year rate and the 30-year rate looks small, it’s applied to the entire mortgage balance. The higher investment return on the difference in monthly payments is on a much smaller base.

For instance during the first year the 30-year mortgage will cost roughly $400,000 * 0.625% = $2,500 more. Investing $942 a month plus tax savings at a higher return will only earn about $200 more. Paying $2,500 more for the privilege to earn $200 extra on investments is a losing proposition.

Over time, as the side fund builds up, the extra investment return starts to over come the extra cost on the mortgage. But it takes a long time, more than 10 years.

The assumptions in the calculation actually favor the “borrow 30-year and invest the difference” strategy in many ways. First there is risk. The side fund may not be able to earn 5% a year. Even if it does on average over 15 years, there’s a sequence-of-returns risk. If the returns are good in the beginning when the side fund is small but bad in later years when the side fund is larger, the side fund won’t benefit as much. We also assumed the tax savings are invested. If they are not, the side fund will be much smaller. We also assumed perfect tax efficiency. In reality the side fund will have to pay some taxes along the way.

Even with all the favorable assumptions, for a $400k payoff the difference is also very small. After 15 years, Bob is better off by about 2.5%. Not 2.5% per year, 2.5% total over 15 years.

I would take the sure thing in a 15-year mortgage for its lower rate. A slightly lower rate on a large balance makes a bigger difference in absolute dollars than a higher return on a small balance.

Note this is not a typical “should I prepay my mortgage or invest” situation. Merely prepaying your mortgage does not lower the rate on the entire outstanding balance. You get the lower rate on the whole balance only when you make a firm commitment to make a higher monthly payment each and every month. It’s a gift to the committed.

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AM says

Good post, thanks. I did a similar calculation and decided that I am much more comfortable carrying as little mortgage balance as possible.

In fact, I am currently refinancing from 15-year fixed into a 30-year 7/1 ARM, for a lower rate (and no cost, of course). I will keep paying the same monthly amount (actually I am increasing my monthly payment), in order to pay off the loan faster. After 7 years my principle will be small enough that I will simply pay it off if rates jump too high. Plus there is a good chance we will move within 7 years. PLUS it gives me more flexibility in case I experience cash flow problems.

Dan says

Great and timely article on a great website! I especially like this point that you made: “A slightly lower rate on a large balance makes a bigger difference in absolute dollars than a higher return on a small balance.” It could take a long time to come out ahead by investing the difference because the amount starts out so small.

There are so many variables to consider in this decision. If an investor is an appropriate age, they could invest the difference in globally diverse set of index funds in a Roth account which would offer protection from future taxes provided that congress does not change the rules on Roths.

Life has thrown us a few curve balls already and as much as we try to plan, I just have no idea what is coming around the corner. The lower payment keeps more options available. For example, if we have to move due to a job transfer, the lower payment may allow us to rent our house out instead of selling it at a potential loss.

There are risks involved with both the 30 and the 15. By investing the difference, we still have the ability to access the money and have control over it. I don’t have a crystal ball, but the 30 seems less risky to me and it is possible that we may come out ahead in 15 years by investing the difference.

Ace says

TFB – I wonder if you could do a breakeven analysis on a related topic. I’ve used your “resetting the clock” calculator to analyze the difference between sticking with my current 30-year mortgage at 4.00% (with 28 years left), versus refinancing to a new 30-year at 3.625% (at zero cost, of course). Your calculator tells me that if I keep making same payment, effectively prepaying my new mortgage a little each month, I’ll pay off the new mortgage in about 26 years and save $40k in interest. Alternatively, I can simply pay my new mortgage off according to its own terms and still save about $10k in interest over the 30-year life of the loan.

My question is this: Is there a breakeven point for these two scenarios? Although nothing is in the foreseeable future, statistically I likely will not pay this loan for its duration. Chances are, I’ll move in 5, 10 or 15 years. If we sell in, say, 10 years, will I have saved or lost money by resetting the clock?

(I actually plan to do something in between the two scenarios with my monthly savings: For the next few years, I intend to put my extra $100 per month towards paying off higher-rate student loans. After those are gone in about six years, I’ll pay my old payment towards my new mortgage.)

Dan says

Ace,

If you are refinancing to a lower rate and it will cost you nothing to do so, it seems to me that you’ll come out ahead right away as they are both 30 year terms. The bank may be able to set your term to 26 or 28 years, if you prefer.

Or, if you have enough equity, you may consider taking some cash out to pay off the higher interest rate student loan debt.

Another thought, once you get within a year or so of paying off the student loans, is to transfer the balance to a 0% credit card. We paid off a property that way. We only had to pay a $100 transaction fee and it was 0% for 12 or 18 months. Read all of the fine print and make sure that it makes sense to do so.

Investor Junkie says

TFB,

I while I agree with the formulas, I disagree with the numbers entered. If you are going out 10-15 years shouldn’t you go with the historial average return of 7-8%? That changes your numbers quite a bit.

What seems of greater importance is your age. If you have 20-30 years till retirement you more than likely will come out ahead not getting a short term mortgage. While there is no guarantee of returns for any investment various issues could also happen with paying down a mortgage faster as well (property going down in value, inability to get money out of an illiquid asset, etc.) So paying down a mortgage isn’t risk free either.

I also posted an article similar to this one and came out with different results.

http://investorjunkie.com/13979/fool-prepay-mortgage/

Investor Junkie says

Let me add while both 15 year and 30 year both are tax deductible, the 30 year gives slightly more back since there is more interest expense. So compared to the two you would get slightly more back at the end of each year. Not enough to dramatically affect the decision of mortgage term, but really a consideration with your effective taxable rate.

Financial Advice for Young Professionals says

This is a very complex and detailed analysis that I think you could skew towards either side based on the assumptions one makes. Personally, I like the flexibility a 30 year mortgage gives. I don’t like investing my after tax money in stocks so I choose real estate instead. And one of the benefits of real estate is you only need to put 20-30% down and you can still get 100% of the returns on capital appreciation(with thanks to the banks for the rest).

Harry Sit says

@Ace – Mortgage Professor’s calculator 3a does the type of breakeven analysis you are looking for.

Student2 says

First, I would like to say thank you for such valuable information! I was lucky enough to stumble across your site while researching Roth IRA conversions and have now read enough to know I will be back! Thanks for your contributions and valuable insight.

Second, regarding the 15-year mortgage vs. 30-year mortgage + investing the difference, it seems to me that the key assumption here, as Investor Junkie alluded to, is whether the investments you are making are tax-advantaged long-term retirement-type or not. If you are considering whether or not to invest additional money into a retirement account, then it looks like a no-brainer to me (and I’m fairly green so maybe I’m missing something). The increased return at longer investment periods is clearly going to have a huge impact on the total available at retirement. The paid off mortgage and deferred contributions (assuming you will begin investing the mortgage amount + the side amount when the mortgage is paid off) will take longer to get you to the same place (and make for a lot scarier ride).

On the other hand, if the side investment is for something else with a shorter period, specifically for less than 12 years by your calculation, then, by all means, pay off the mortgage first.

In short, other assumptions on returns, etc. aside, the key point is the investment period.

Harry Sit says

Student2 – I agree if paying a 15-year mortgage makes you unable to fund tax advantaged accounts adequately or max them out, you should not get a 15-year mortgage. For those who can do both, it’s a viable option versus investing in regular taxable accounts because you get a lower rate on a large sum.

bcarney says

“We assume Bob earns 5% on his side fund.”

Where the hell is anyone making 5% on anything that’s non-gambling risk?

Harry Sit says

bcarney – I know some want me to use a safe, guaranteed rate of return to compare to the certainty in paying off debt. Some others, as in the comments by Investor Junkie above, want me to use a higher “historial average return of 7-8%.” I just picked a middle-of-the-road 5%, not guaranteed of course, but likely achievable in a diversified balanced portfolio. The linked spreadsheet allows anybody to plug in their own assumptions.

Lily says

Great article on a topic that many people have never given serious thought to. Given that 30 year treasuries are only yielding 3%, I think 5% is a reasonable guestimate for medium risk investment return. Most people sell or refinance in less than 10 years so it seems like investing the difference is a risky move that is unlikely to yield rewards.

Heidi says

Thanks for a great post! I ran my own model, and agree that I’m better off refinancing to a 15 year mortgage rather than pre-paying on the 30 year or making the regular payments without refinancing.

I like this blog. It makes me think!

Marcus says

Another thought to take this out further would be to have the person with the paid off 15 yr mortgage immediately invest the freed up monthly mortgage payment of $2,859.53 into the same investment and assumptions that the difference has been going into and see how long this takes to catch back up or if it even would.

Shawanda @ You Have More Than You Think says

I think it’s interesting how confident people are of their ability to find an investment that generates higher returns than the effective interest rate on their mortgage.

Also, I wonder how many of them actually get around to investing the difference that’s going to yield them all these stellar returns.

bp says

Let’s not forget all of the young professionals with over $100,000 in student loans at and unshakable rate of 6.8%…and there’s a lot of us! Do the finance gurus out there realize that the graduate student loan rate is that high?

Anyone in that situation should be advised that a 30-year mortgage is a no-brainer.

JoeTaxpayer says

The higher rate on the 30 does cost you. If the 15 year leaves enough money each month that the risk of needing to borrow at a higher rate is minimal, I might agree to go 15.

What I’ll take issue with are those who are so extremely anti-debt that they forgo matching 401(k) deposits, claiming that after 15 years, they’ll have a huge monthly deposit they can afford. Or those whose budgets are tight to begin with, and think the numbers work in their favor by paying off their mortgage faster while still owing money at 18%. I dare say, the sub-4% mortgage money may be the lowest rate we see in our lifetime. When rates go back up to ‘normal’ it would be nicce to be buying 8% CDs while paying the bank 4% for years to come.

bp says

Also…

Most arguments of 15-year vs. 30-year mortgage ignore the performance of the asset i.e. the house. You are assuming more of the risk when you choose to put more money into a house on a 15-year mortgage. If the house value goes up, this will work in your favor. If it goes down, however, it works against you because now the bank has more of your money than if you had chosen a 30-year mortgage.

Tim Richmond says

This is a fascinating analysis. I wonder if home buyers in general would be less confident with investing the difference simply because it is psychologically more satisfying to pay off something so tangible like a home.

Lee says

I was reading about mortgages on your website, what I do is I borrow $10,000 from my paid off car and place the money down on my mortgage. As soon as I pay the car loan off I borrow from the car again. I save big bucks from reducing paying interest on my mortgage.

J says

You are forgetting one vital factor – Inflation.

While I am paying a large dollar value for the first 10 years, the value of the money changes over time.

In a 15 year loan you are paying more in terms of nominal dollars upfront, where as in a 30 year loan you are paying much less because inflation has eaten away the value of that dollar.

Since the majority of interest on a loan occurs in the first 1/2 of the term, you get to deduct the highest nominal dollar amount – then reap the rewards of your 5% investment later (minus inflation at 3%). Otherwise you are just paying today’s dollars upfront in principal with minimal benefits in terms of rate reduction.

Harry Sit says

The analysis compares the value at the end of X years. You look at the amount you still owe, offset by any investment side fund. Whichever strategy makes you owe less at that time wins. It’s not affected by inflation, unless you say inflation drives the investment return. If you assume a 15% return instead of a 5% return then sure, invest the difference wins.

Ben says

Harry,

Thanks for the article. Two points, the mortgage interest tax deduction is not well understood. The statement “Because Bob pays more interest in the 30 yr he gets more tax deductions.” while technically correct, should take into account the interest cost vs amount of deduction. Since a dollar in interest paid reduces taxable income by a dollar. One pays a dollar in interest to avoid paying $0.15-0.35 (marginal tax rate) to the government.

Second,

The 15 and 30 year examples have differing amounts of leverage. One is not just comparing a net dollar amount to determine which option is “better”, but one needs to consider the increased risk as well. This increased risk is understandably hard to value numerically, but should be considered none the less.