## Monday, August 27, 2007

### Paying down the mortgage early?

OK, there have been a couple of posts on the blogs that I read discussing the benefits of an early mortgage paydown vs. an alternate investment.

And me, well I'm kind of a chump, so I ran the numbers quickly. For reference, this is a 200k fixed mortgage at 6% over 25 years. Here's what the monthly breakdown looks like for the standard mortgage. That Purple Stuff is the money the bank is taking for interest which, as you may know, is mostly taken first. And the Light Tan stuff is what you're actually paying down. For the last two, I've taken an equal size payment (~\$4600), off the principal at different points in time. So that Blue Strip on the last two is the amount of interest that you save each month as time goes on.

When you pay down interest early on, things change like so:

Paying things down late gives you something like this:

Now, the original posters were talking about applying extra money against the principal and calculating the interest saved as a percentage of that principal. So if I paid down 10k on a 6% mortgage with 10 years left, I'd basically be saving \$600/year or \$6000 in interest.

However, the graphs would seem to imply that something terribly different is going on here, I mean, you can only save chunks of the purple stuff and if you're paying down the mortgage later rather than sooner, there's a lot less purple stuff to save on.

Imagine it this way: say you took out 100k @ 10% for 10 years and made your regular monthly payments (\$1321) for a full year. Then, magically at the end of the year you win the lottery and pay down the house in one swoop, how much would you pay? A quick run to my information source, indicates that you still owe \$93.8k, you were going to pay \$58.5k in interest on that mortgage, but you paid \$9.7k in interest in the first year alone, the bank took 16.6% of the money you owed them in the first year. In fact, in the next year, they would've taken \$9.1k which was 15.5% of what you owed them, or 18.6% of what was left. By the end of two years, they have 32% of what we owed them, that's 32% in only 20% of the time.

So let's back off and go to our equation. Both posters are saying: if I drop 10k on a 10% mortgage I'll get a return of 10% times the number of years, and I'm saying that the calculations are flawed. So we'll use the 100k @ 10% for 10 years example to make life easy, if I put down 10k, it will "earn" 1k/year. Let's say that I get to my final year and decide to put down the 10k. With 12 months to go, we've paid 57.7k out of 58.5k in interest and we owe 15k on the place.

Wait, hold on right there! we're supposed to save 1k in interest, but we don't even have that much owing in interest. If I put down my 10k, I'll still owe 5k on the house, but I won't have saved 1k in interest, there's not even 1k in interest to save! What if I do it the previous year? At this point I owe 28.6k on the house and I have 3k left in interest to pay. So now the model is telling me that I can save 2k (or 2/3 or the remaining interest) by paying 10k of the 28.6k principal that I still owe (or more than 1/3)?

If the numbers seem weird, it's b/c they are, I mean, they're clearly wrong. You're not going to save 66% of the interest over 2 years by paying down 35% of the principal, that's pretty clear.

What's going on here is equally clear, if you're at the end of the 10% mortgage, you're not actually paying 10%. In the last 2 years of the 100/10/10 example, you will normally pay 31k into the mortgage and only 2.3k will go towards interest, i.e.: you only pay 2.3k/28.6k or about 7.5% interest. If you're in the last year, that number drops to like 5.5%. Here's the "effective interest" chart:

At the start of year 2, the 100/10/10 mortgage owes 93.8k, but will only pay 9.1k, which is actually just under 10%. So where did the original posters go wrong? Well, you can't "save" 10% interest if you're only paying 7.5%. The other problem is that the 6% is relatively small, so it's easy to gloss over the math. In the 200k @ 6% for 25 examples (the first graphs), you're actually paying between 5.15 & 5.95% "effective interest" for the first 22 years, so you can basically just gloss over the number (even if it's wrong) b/c you're still within a percentage point. If interest rates go to 10%, then suddenly you're losing whole percentage points and the bad math becomes evident.

So after a few hours of number crunching, what do I think? Well, the basic premise of both posts is actually still good: where am I going to get better returns? And the simple answer is that all things equal you'll get better returns from whatever is paying/charging the higher "effective interest rates". (where the "effective" part is key)

However, right now, things are pretty muddled b/c today's interest rates are yesterday's mortgage rates. This is complicated by tax law. You see, in Canada, we get tax breaks for RRSP investments and in the US you get tax breaks for mortgage interest. So in Canada if you have room to contribute to your RRSP (they do have caps), then you actually get an immediate 20-40% return on putting the money in the RRSP. In the States you'll only get a tax break for a certain period at the beginning of the mortgage, and then the interest will become too small. All in, the numbers could really "go either way" so there's no clear winner.

Personally, I'd rather have the money in something liquid and diversify. "Cash is King" and your home isn't bringing in any cash (unless you're renting rooms). Give the cash to someone who can make you more cash and if you're still itching to pay down the home then use the income from that cash to help with payments. At least this way you're making and spending money rather than just spending it. That way you can redirect the cash flow if you need to.

telly said...

Gates, I clearly expected your summary to state that if you're going to make pre-payments, make them early rather than later and then you threw me for a loop! Did I misunderstand your post?

Anyway, good analysis, even if I do take something else from it. :)

Gates VP said...

You know Telly, I think the missing component in the first 3 graphs is actually the value of inflation.

You're kind of right in that paying early has a bigger long-term effect, but if you look at the bottom graph you get to see what's actually happening. If you pay down a full year of principal, you're just skipping ahead a year on the interest chart. That's what I mean when I say that paying down 5k now is actually paying off the last 5k. (i.e.: today's dollars to save tomorrow's).

If you can earn more interest than the effective mortgage rate, or vice-versa, then it's easy to pick one or the other. But for most people right now, those numbers are very close, at which point you have to start factoring in inflation and the simple value of cash.

If you have mortgage at 4% (from say 2001) start dropping the money into the 4% bank accounts. Again, the last chart shows that you're actually paying like 3.75% so you can actually make money on the deal. Interest rates seem to rising, so if they hit like 5%, you can probably get the best of both worlds and use the interest on the cash to help pay down the mortgage. And that's what I suggest, b/c you're using "somebody else's" money to pay for your mortgage :)

telly said...

Our mortgage is actually locked in at 4.39% but the problem with earning 4.5% in interest income is that it'll be taxed as income again. In our case, in a 43% marginal tax bracket, it's better to pre-pay the mortgage.

Patrick said...

Hey Gates, it's Pat. Interesting post. I would have to agree with your dual RRSP/mortgage strategy. Factoring in the money back with the RRSP investment, it's hard to go wrong with an RRSP unless you are heavy in the equities and the market is taking a serious beating. Even then, if the market is taking a beating, then there is a good buying opportunity on the horizon.
Combine that with renting out a room to help pay the interest component of your mortgage payments, and you've got it made.

Non-registered investments would not make much sense versus paying off the mortgage, especially low return GICs combined with a high tax bracket. Might as well leave the money under your pillow almost.

So that is the order in which I would invest:
1) RRSPs
2) mortgage payments
3) personal investments, short term goal savings, i.e. low risk investments (education... possibly funded with RRSPs)
4) non-registered long term investments and/or any other "riskier" investment that you can think of.
...
10) beer

Funny how I never seem to get to the beer... ;)

Gates VP said...

I like the list. Of course, I'll contend that even that order is a little tough to gauge.

You're under 30 ;), so the RRSP is very safe sink. Of course, one of the original posts is an American blogger, and they just have 401k which like RRSP "light" via your employer.

I would generally put the mortgage further down the list. But mostly b/c the house doesn't appreciate "quicker" if you throw more money at it. Paying down early "feels good" and it's "simple", but I can't really bank it as the most efficient.

But the RRSP concept does bring to light an important question, "are you meeting your RRSP goals?" If you're 55, with 3 years left on the mortgage and you're on course to "retire" in 5 years, then who really cares about something like 5k? Throw it in savings for your new Jag fund and just call it a day :)

Of course, if you're 30 and you get the money with like 20 years left on the mortgage, then maybe even the RRSP donation is a little sketchy. I mean, if you're already meeting your RRSP goals, then maybe it's time to get "risky". If you're 30 and a working professional, it may be time to look at your career. Spending 5k to take time off and do some training could pay way more than any of the other options. Heck spending the 5k on acquiring a second place to use as a rental unit could also generate way more income than just socking the money away.

Of course, it all comes back to risk, go figure :)

Maury said...
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Maury said...

Thanks for pointing this post out to me gates vp. Very good analysis. So if my loan is 6%, it appears as if I'm not paying MORE than 6% early on in the mortgage, it is just that I'm paying less than 6% near the end of the mortgage.

Interesting stuff. For folks in the U.S., it looks as if there becomes a point near the end of the loan where it just makes sense to pay it off as the tax benefit will mostly disappear. I might have to hit the spreadsheets...

Anonymous said...

You are missing one critical component in your analysis of the final years of a mortgage: the amount of principal owed.

In the last year, the amount of principal steadily declines. Since interest is only paid on the outstanding balance, you steadily reduce the amount of interest paid as well.

Using your example where you have 12 months to go, with \$15k @ 10% outstanding, your mortgage balance looks like each month, along with interest owed for the month:

balance, interest paid
Jan: 15000, 125.00
Feb: 13806.26, 115.05
Mar: 12602.58, 105.02
Apr: 11388.86, 94.91
May: 10165.03, 84.71
Jun: 8931.00, 74.42
Jul: 7686.68, 64.06
Aug: 6432.00, 53.60
Sep: 5166.86, 43.06
Oct: 3891.18, 32.43
Nov: 2604.87, 21.71
Dec: 1307.84, 10.90

\$15000.00 principal paid
\$824.86 interest paid

Initially, these numbers work out to show exactly what you claim:

824.86 / 15000 = 5.49%

However, if you take each month individually, the picture becomes clearer:

Jan: 125.00 / 15000 = 0.83%
...
Jul: 64.06 / 7686.68 = 0.83%
...
Dec: 10.90 / 1307.84 = 0.83%

Each monthly, we pay 0.83% in interest on the outstanding balance. Over the course of the year, we paid:

0.83%/month * 12 months/year = 10%

There you have it. Although we are still paying 10% yearly interest each month, in the last year, because the declining balance amount become significant, it appears that the amount of interest is significantly lower.

Gates VP said...

Great insight anonymous!
The numbers are strong with you!

Of course, if we go back to the original premise, does this change the plan?

If I get a 10k windfall and I have 10k left on my mortgage @ 10%, I'm not going to pay \$1000 in interest, just \$549 in the next year. If I take the \$1000 and invest it at 10% (all things equal), then I'll have \$1k in interest to balance out the \$549 "extra" interest that I paid out (minus taxes, 40% of 500 = \$200, I'm still up)

End of the day, it's really close either way, I would personally invest the cash primarily for diversification purposes ("cash is king"). But I can understand a whole host of reasons for going the other way :)

Confused Aussie Gal said...

Hi Gates,
I must be the dumbest person ever because I could not follow at all. I'm not sure if it is becuase I am Australian(probably). But I am looking at changing my home loan from P&I to just Interest ONly and never paying it off. I then want to use the equity to invest in more property instead. Should I be doing this? Property here always doubles every 7-10 years. I am in my 2nd year of a fixed only loan.

What do you think?

Gates VP said...

Hey AussieGal:
I must be the dumbest person ever because I could not follow at all

This is hardly the case. This is in fact a lot of math and honestly, it's poorly presented. However, I think that the answer you seek is not exactly related to my topic here. But I will offer some advice.

What you are proposing to do is in effect a "double or nothing" style bet that leverages the current value of your home. On the risk scale of 1 to 10, this is a 9 or so.

If everything goes well in the housing market you get a ton of "easy money". If the housing market collapses, you could end up with no houses, no equity and be in debt to the bank.

Property here always doubles every 7-10 years.

Your use of the word "always" is extremely discomforting. There is no "always" and your proposal of doubling in 7-10 years does not have much historical precedent. They may not be "making more land", but it's not like Australia has any significant shortage.

For a house to double in value in 7 years it must appreciate 10%/year. Inflation in Australia is averaging about 3%/year. That's a 7% differential. That will quickly "lock-out" any new home buyers (buyers with very little equity) as houses simply become "too expensive". That situation is not likely to last for very long, so it's highly unlikely that your house value will continue to double at that rate unless inflation becomes very large (at which point the doubling is useless).

Again, the best advice that I can offer is that you are pushing a 9 on the risk scale. If you are comfortable taking that risk, then go ahead.

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