After the interest rate drama last week, I managed to lock in a refinance of my current 30-year mortgage (with 26 years left) which had a 4.75% fixed rate into a new 15-year mortgage at a 3.875% fixed rate. You’ll probably see lower rates in ads and elsewhere, but it did come with negative points that offset my closing costs completely and then some. Anyhow, I wanted to run the numbers to see the potential financial benefit.

To simplify the numbers, I am just going to assume a new mortgage with a loan amount of $300,000. First, we have a 30-year fixed rate with a lower payment, but higher interest rate and longer period of paying interest. Now, we do have the option of making extra payments toward principal and making the loan end early. Alternatively, we have a 15-year fixed mortgage with lower interest rate but higher mandatory monthly payment. There are many calculators out there, but I still like the simple and familiar ones at Dinkytown.

The 30-year at 4.75% would have a monthly payment of $1,565, while the 15-year would have a monthly payment of $2,200. Now, what would happen if we simply paid the $2,200 towards the 30-year mortgage? Using the calculator, we would enter an additional monthly payment of $635. That tells us the 30-year plus extra mortgage would be paid off in 16 year and 5 months, requiring an additional 1.4 years and $36,000 in interest. However, the 30-year does allow me the flexibility to reduce my payment by $600 a month if needed.

**A note on interest paid.** Lots of people simply look at how much interest is paid on a 30-year and compare it to a 15-year. It’s a big difference! However, you have to remember that you could have done something the money saved each month from a lower monthly payment. Theoretically, if you went out and bought a bank certificate of deposit paying the same rate of interest as the mortgage, there would be no real difference. For example, currently Discover Bank has a 10-year CD yielding 2.25% APY (see CD Rates & Calculator tab). This makes the true interest gap less than what it may appear. Still, there isn’t anything available at anything higher than 4.75% or even 3.875%, so I’m still happy to pay off this house in 15 years.

excellent comparison – you are right in that most people just “eyeball” estimate the math. great lock for you!

Thanks for an excellent job of number crunching.

When we refinanced about 2 years ago my wife and I went with the 30 year plus an extra monthly payment because of another factor that can be extremely important. That factor is flexibility.

My wife is a teacher. During the 8 1/2 months that she is working we send an additional $750 towards the principal. However, during those long summer months when we are a one income family it gives us plenty of breathing room by just paying the regular monthly payment.

Unfortunately, I don’t think this is especially helpful. You were not looking at refinancing to another 30-year at 4.75%, so you’re comparing apples to oranges. Since all mortgages front-load the interest, you need to account for the 4 years you’ve already paid interest and look at the remaining interest only. You’ve already probably paid in a pretty good chunk and the difference between adding the 635/month extra should make it less than you’re showing and maybe less than the 15 years. I agree that most people don’t look at the shorter term when refinancing and reset back to the 30 year, so I like that, but maybe you should compare to one of the more special products like a 20 or 25 year in addition to the common 30 and 15 year.

I just went through the same situation on a refi and went with a 30 year that I’m prepaying on a 20 year schedule. You may want to take into consideration the tax implications of both – there is more interest to be written off on your taxes with the 30 year, which is very beneficial and lowers your borrowing cost. Also one more point – the lower monthly payments of a 30 year shown on your credit report will help you qualify easier for any additional loans down the road – ie – rental property.

Scott, I have to disagree. This is an apples-to-apples comparison in terms of cost savings going forward. What has already been paid is a sunk cost.

Jonathan is looking at the amount of money that can be saved moving forward. Accounting for interest already paid is moot.

nice comparison. it would have been very helpful if you also included another couple of aspects like another 30 year with a lower interest rate since they have dropped and in addition 20 or 25 year like scott mentions. Your articles are very helpful

Thanks for the analysis. Would also be interesting if income tax deductions for interest were considered.

Taxes?

Liquidity premium?

Discount rate (inflation)?

I Refi’d from a 4.75 30yr to a 3.75 15yr at no cost a few months ago, but the decision was/is far from clearcut and it is impossible to know the better financial decision ex ante.

At a 33% marginal rate the 1.00% of rate improvement drops to 0.67%.

So the question is, do you believe that a savings of 0.67% is adequate compensation for the loss of liquidity (and leverage) in making this change.

That answer requires making some difficult assumptions especially given the front loading of interest and thus the nonlinear tax effects.

Nevertheless with an inflation rate at 2.0%, the 15 yr is better. If, howver, the inflation rate is 4% over the next 30yrs, the 30yr would have been the better choice.

In my case the liquidity premium was negligible and while I felt that the currently low inflation rates can’t last forever, I was willing to take the risk of future inflation in return for a known real rate of return (at 2% rate of inflation my after tax real rate of interest on the mortgage is approximately 0.5% in my tax situation).

Looking at the nominal dollar analysis as you have done is a good first step, but of course the most important factors, as always, are out of our control.

Personally, I wouldn’t count on the income tax deduction going forward. If congress REALLY wants to cut the deficit, the big itemized deductions (interest, charitable) will have to be cut big time.

Also, many people don’t realize that the home mortgage deduction only does you any good if you have OTHER itemized deductions (taxes, charitable, etc) that exceed the standard deduction ($5,700 single, $11,400 MFJ). So, for example if you’re married and have $5,000 in other deductions, the first $6,400 of home mortgage interest gives you no benefit on your taxes.

what about the prospect of higher interest rate down the road? (higher CD rates as well as borrowing cost) May be you should lock in a lower rate now for as long as you can. Not to mention the affect of higher inflation. I bond annual rate is higher than the 30 year mortgage now.

Jonathan,

I did not run the numbers but refinancing from a 30yr loan to a 15yr after 4 years of paid interest could make sense. I think you waited a little too long for this.

What I did not get is why such a high rate? As I mentioned last week amerisave.com (and others) offered 3.37% (and dropping) with the closing costs fully paid.

Also, why did you get a 30yr loan to begin with? After all, you and your wife make each over 100k, haven’t reached your earning peak yet, don’t have big liabilities and the loan was less than $500k. All these decisions seem kind of too conservative to me.

This is generally how I decide to refi. Maybe not the most scientific, but if I can pay the mortgage off sooner with the exact same payments, it’s a bit of a no brainer. (But, we are in for the long haul – don’t plan to sell before 30 years, etc. More analysis is needed for somone who will probably move in the neat future – maybe not worth it).

We just did a similar analysis, but shaving one year off the mortgage didn’t feel worth the bigger mortgage commitment. We decided against it. That said, I am getting closer and closer to the fence. The payment isn’t really that much at 15-year, but with the economy as it is, and how our health insurance is really hard to pay (skyrockets out of control every year), I know that it’s not the best choice for us at the moment. My spouse has not worked in a decade though. If he were working, it would be a no-brainer. I am hoping we can refi at these rates in the next year or two. (Certainly not holding my breath – but might make more sense then).

I, too, am also surprised at the rate you did settle on. If I were in your shoes, I would get the lowest rate possible (pay points, closing costs, etc.). You have the cash to do so. I’d take FULL ADVANTAGE and lock in the lowest rates of the century. I am generally not a fan of paying points, but these are rare times. I’d pay some points to lock in 3.25% or whatever is out there, personally.

I am in the process of converting a 5.75% 30 year loan into a 3.875% 15 year loan. (It is a rental, thus the higher rate despite my 840 credit score…)

The key for me was break even point. I added $3000 in closing costs to the new loan and just looked at the amortization tables of both to see when they were equal. 12 months from now, I’ll owe as much with the new loan as I would have with my old loan.

(That said, I have to pay a bit more on the 15 year loan ~$90 per month, so that is about another $1000 (12 months of paying an extra $90) that I need to factor in. All said, my breakeven point is about 15 months.

I’m curious if Jonathan ran a breakeven point analysis…

@scott – I see your point in that the benefit difference is probably less, but the basic idea is the same. The 15-year would still result in less interest than a 25-year refi + extra, but with less flexibility, given the current interest rate environment.

@P.T., nellcat – Taxes are hard. Very situation dependent. It all depends on how much mortgage interest deduction you have left after your standard deduction and other itemized. Standard deduction for married filing jointly is $11,600, while $300,000 x 3.75% = $11,250 and goes down every year. Unless you have other deductions or big mortgage, you might not get any tax benefit at all.

I do like your point about lower debt, and we counter that by only having one of us on the mortgage.

@enonymous – I mentioned the liquidity aspect, but I’m not sure how I could quantify it further. If you’re going with the 15-year, you must want to pay it off in 15 years or less. Liquidity is a benefit of the 30-yaer, and you just have to weigh it with the added cost, which I have outlined. Also as noted above, taxes are not always as easy as just the marginal tax rate.

@Pat – I agree, one of the proposed ideas is to get rid of itemized deductions and replace with lower overall tax rates. That sounds like way too much compromise for our “leaders”, however.

I would add that each year the standard deduction will go up due to inflation, while your interest paid will go down. So your tax benefit will drop every year. Oh, and the 2011 standard deduction is even up a bit $5,800 single, $11,600 MFJ according to IRS.

@steven – That is a possibility. We should definitely lock in low rates if we can, but I don’t want to delay paying off my house now in the hopes of high rates down the road. Once my house is paid off, I can buy CDs or bonds paying good rates if the interest rates end up really high in 15 years.

@Adrian – You may be right, I do tend to be conservative but that’s just how I like it.

Congrats on your nice low rate! I am jealous. 🙂

You should add a column in your analysis if you pay your 30 year mortgage on a 15 year schedule and add the refinancing costs into interest in the new mortgage. I would be curious too see those numbers.

I guess my point was: according to amortization tables of the original 300k @ 4.75, interest totals for the first 4 years equal $55k. This amount of “sunk costs” isn’t taken into account in the comparison scenario. So, instead of the high-end estimate of $263k of interest payment versus the pay-ahead plan at $132k, it’s closer to $200k if the extra payments were applied now. This should improve the $132k number to closer to $96k as well as shorten the time frame from 16 years 5 months to closer to 15 years too. I just don’t see how you can ignore the fact that you’re 4 years into table since the tables are not linear and do not extrapolate according to these term-of-loan calculations.

Amortization tables are not linear, but they roughly correspond with the interest rate being charged on remaining principal. For example if your $300k principal at 4% interest, your first year of payments will have $12,000 in interest included. The rest goes towards principal reduction. The next year, your principal amount is lower, so less goes towards interest, and so on.

In year 5 of my 30-year loan, I would again be paying interest roughly equivalent to my interest rate times principal remaining. Interest is only “front-loaded” to the extent that you owe more money in the beginning.

Basically, this comparison still applies. The principal amount remaining will be smaller than when I first bought the house, but will be the same for both loans. If I had 300k in principal left, these are the numbers I’d be looking at. You could run the number with $275k left if you wanted. I could also add a 25-year option.

I’ve noticed that a lot of people just don’t look back at what they already paid in interest when calculating the efficiency of a refi.

Labeling it as sunk cost they just want to feel in control by taking some financial action a do a refi without adding it to the equation.

Isn’t this one of the financial behaviors so much described in the financial planning texts found more in market investments?

In the end everybody does what it please and if overpaying in interest makes somebody feel better than why not.

Actually, not ignoring sunk costs is the irrational behavior discussed in behavioral economics. If you’re being rational, you should ignore sunk costs.

http://en.wikipedia.org/wiki/Sunk_costs

Scott,

When considering a refinance, it may make a great deal of sense to calculate the new loan payment as if it were for the exact number of payments as your current loan has remaining. Example, you are 50 payments into a 30 year, then calculate what your new loan would be if it were for a term of 310 payments. Whichever payment is lower is the loan which will cost you the least. It is easy enough to use an online payment calculator in order to compare the two.

But when it comes to interest already paid, that was just the cost of owing money to the bank. It doesn’t matter what interest you have already paid any more than it matters what you spent on utilities last year. It was an expense for something which you have already used (owing money for a period of time).

You also have to remember to factor in the marginal tax benefit of the interest that you pay. The impact of the interest paid would be the interest * your marginal rate= tax benefit. For the thirty year $263380*.35=$92183 tax benefit assuming you are in the thirty five percent bracket. This compares to a much smaller 33619.95 net tax benefit on the fifteen year.

To me w/ the flexibility of the 30yr plus the tax benefit sounds good.

Couple of things. If you get a 3% 10 year CD, you would be paying taxes on them. Assuming an approximate 1/3rd tax, your net return is about 2%. Also, the difference between the two loans of $36k doesn’t take into account the tax deductions. Assuming, you are above the standard deduction and a 1/3rd tax rate, you get $12k back in tax deductions, so effective difference is about $24,000 over the time. There are definitely too many variables here, and we need a proper statistical model to actually take into consideration the residual effects of various parameters. But at the end of the day, it is all about the person’s comfort level and how they perceive their money

Over the weekend I bit the bullet and locked. We’ll be going from a 30-year at 4.875% (2 years in) to a 20-year at 3.75%. Could have saved on closing costs with a higher rate, but decided to pay half a point to get this rate. My payment will only go up about $100–but I’ll pay the loan off 8 years sooner and save about $120,000 in interest (about half of what was remaining on the 30-year). Maybe we’ll be able to retire in Kauai after all!

I’m hoping to be able to re-finance in 2013 or thereabouts. Right now our equity level is so low that to re-finance, we’d have to either bring a big lump of cash to the closing or pay PMI, which we don’t currently do because of having put 20% down originally. With the fed announcing that they’re going to keep rates low for at least another 18-24 months, hopefully a combination of paying down the mortgage and a stable (maybe even slightly uptick?) housing market would allow us to be able to do this.

If that works, I’d definitely be going to the 15 year option assuming rates stay the same.

Which site did you use to find your mortgage? Anything new in this area?

I wonder how much your calculations would change if you took into account the time value of money (and assumed a three percent inflation rate) when calculating the present value of paying future interest?

Ok, so I learnt something here … the economists say don’t consider the sunk costs when taking a decision … might make sense in their examples but I’d say you need to look at it from a different perspective:

Compare the sum of remaining interest left to pay with the current loan with the total interest of the new loan and refinance if the new one is lower.

This way you don’t need to know whatever was already paid in interest.

Here is a calculator that sums it all: http://calculator.net/refinance-calculator.html

Thanks everybody and good luck!

Good point — you need to look at the present value of the interest paid and not simply the nominal value, as well as consider the opportunity costs of said payments.

What about the discounted rate of the money? For example, I am paying $1000/month now, during year 1 and will still be paying $1000 for my last payment 30 years from now, only 30 years from now the value of $1000 is quite a bit less than it is worth today. You lose that benefit when you go to a shorter loan period as you are paying more per month *and* not reaping the ‘benefits’ of inflation.

How do you account for it in your decision making process? I understand some of the discount benefit of a longer loan are offset by less interest paid in the shorter term loan. But how did you pick the discount rate?

The discount rate I would compare with is simply the interest rate on the mortgage. For example, do you expect to beat 3.75% over the next 15 years? At what risk level? Are you certain you could beat it? A US Treasury bond with 15 year maturity currently pays 2.75%. Other things pay more, with higher risk.

If high inflation occurs, it is true that a 30-year mortgage could provide an inflation hedge. But you’ll be paying for it in the form of extra interest for that hedge, and it may not payoff. Is it worth it? Again, that is up to the borrower.

J-

Interesting points for sure. Regarding payment flexiblility, one point you fail to mention is if your family moves to one income as a result of you eventually moving to one income as a result of children. You lose out big time in flexibility in the option you choose and Scott has obviously pointed out that your move to a 15 year is good blogger fodder, but really a wash at best financially no matter if you consider an amortization table linear or not.

My point being; did you and your wifey (who earns great money and has a substantial career) consider the impact if you or she were to consider moving to a stay at parent mode? Since you’ve moved the blog away from insight into your personal financial growth and more into higher level topics it would be interesting and not to invasive to learn how you evaluated this decision from a family planning perspective.

I don’t if I would call saving 1% a year on mortgage interest ($4,000 the first year on a $400,000 principal amount) a wash. But yes, either of us could afford the new 15-year mortgage payment on our salaries alone. As to family planning, paying off the house will also allow us to have no mortgage payment by the time college rolls around. I can only hope college won’t cost more than the old house payment by then!

As you pointed out, I guess that really depends on the perception of the borrower once you factor in some of the other points brought up by others. Given the delta in the rate (sizable, but not huge) once you consider some of the other points raised (inflation, loss of flexibility, potential tax savings depending on your situation) you can make the agruement both ways. You’ve done a great job of illustrating both sides of the coin for us and regardless you will be done sooner vs later.

Just wait until you really peel back the onion for yourself (and us!) on college savings cost. You won’t believe it and I would bet that prepaying college (some states offer prepaid tuition plans as far as 18 years out) saves much more than prepaying your mortgage.