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.