Daily Links: Compound Interest, Web Income, and Happiness

In light of the previous post about paying off your mortgage early (http://finance.yahoo.com/expert/article/millionaire/39312) and this current post, I’m wondering what GRS’s official position is with regard to mortgage payments.

If compounding interest on an investment with a rate higher than your mortgage, aren’t we then best served not putting additional money towards the mortgage and investing it elsewhere?

Or should we find a ratio whereby additional payments are made on the principal as well as are invested?

Should we change our strategy when we do not expect to live in the house after (or even close to when) the mortgage is paid off?

Let me write this in simple words:

This is inaccurate.

There are 2 factors for this:

1. a long time can be a long time

2. there is a problematic assumption that makes it so, the fact that you just pay everything at the end.

Lets look at the above example with 30 years:

1. Invest 100K at 5%
100 * 1.05^30 = 432K

YOU MAKE 332K (you had 100K to start with)

2. Invest 100K at 9% + Borrow 100K at 6.5%

Naive calculation:
100 * 1.09^30 = 1327K
100 * 1.065^30 = 661K

so, 1327 – 661 = 666K

YOU MAKE 666K (about double the previous scenario after paying off your loan).
THIS IS WRONG since life doesn’t work this way. You have to make payments on your loan, so that interest you are compounding actually doesn’t compound.

On a simple calculation, you’ll find out that your monthly payments on that 100K loan at 6.5% are around $632. So on the first month you’ll actually make around $750 in interest, which means your 100K will be $100118. Those $632 you payed for your loan are not earning money for you with your high 9% interest.

So, scenario 2 looks like this:

year 1: investment 101K
year 2: investment 103K
year 3: investment 105K
…
year 10: investment 123K
…
year 20: investment 187K
…
year 30: investment 316K

So, summary:

Your 100K makes you 332K
Borrowing 100K makes you 316K

So you’re better off with option 1.

(this assumes the values posted in this article and 30 years for both loans and investments)

If we look at the example with 40 years though, things look a bit better:

Your 100K makes 604K
Borrow 100K makes 972K

My point is that in the original article the simplification is too much and gives the wrong impression.

There is also the problem of why would you have a sure 9% investment in one case and only a 5% in another?

Conclusion, always run your numbers, don’t take someones word. One thing is true, compounding is a powerful force, and it’s better to have it on your side (investing) and not against you (loans).

Californian — you’re right, it was a naive calculation. However, if you take into account tax deductions from a mortgage, it might tip the balances in favor of the other option (even with the non-naive calculation). I could be wrong about it.

Also, had I tweaked my initial numbers a bit more it’d be heavily in favor… say I took 11% vs 6% borrowing rate. But, I digress.

Anyway, I do want to be clear that I never intended to mislead anyone. On my blog, I definitely say up front that I’m not qualified to give any financial advice. And, I still stand by the math… though you’re certainly right, the long term can sometimes be a lot longer than people think. Ultimately, the amount of time required is dependent on the two rates (borrowed vs investment return).

The main point that I wanted to get across was that it’s not intuitive. Most people (probably not you) tend to take the difference between the rates and assume that is what you’d actually be getting over the long-run.

In any case, I’m glad you did the non-naive calculations, and I do hope that others at least got to think a bit more about it.

In reading a lot of finance blogs on this subject, they have always mentioned around a 10% interest rate that is compounded.

What kind of investments would return this? I assume that this is investments related to stock, unit trusts etc.

Currently the uk base rate is at 5.75%. The best rate from a special tax free Savings account called an ISA in the UK is 6.30%

You can get savings accounts for 8% but this is only for a year and usually capped to balances of around £2500-£3000.

If these rates are for stock related investments, they I can’t see how you can count on having these returns each year.

In fact if you have a bad year you could end up losing money.

I kind of new to this so I’m interested in what kind of investments people are talking about when they have 8%+ returns

The reason why this doesn’t work for me is also the reason why I would pay off my mortgage every time: There is no such thing as a sure investment return.

What you are talking about when you talk about return on investment, is actually the *potential* return on investment. Your investment might do 8% every year for 25 years, OR it might lose money some years. You can’t possibly know which.

Even paying off the mortgage is a *potential* 6.375% return for me, but its less risky than most *sure* 8% returns.

Of course feel free to disagree, but, in my experience the world works on fuzzy math. I would rather potentially hit my crossover earlier by paying my mortgage off earlier than potentially be paying it into retirement because I also have to pay down debt from bad investments.

This is precisely why companies that expect a high ROI should borrow large amounts at low rates… they would make out like bandits.

—————————-
This is also a questionable statement. Companies, like everyone else, borrow based on the assets they have, and their credit ratings are adjusted appropriately.

Consider Microsoft, who has next to no hard assets, other than a few buildings. They have a huge ROI and next to no debt, and they would not get that great of terms on debt because their primary asset is human capital, which doesn’t go for much in a bankruptcy.

Verizon on their other hand, has covered the nation in cables, which sell for top dollar in a bankruptcy court, so they have a pretty high debt ratio.

Finally, the very weathly follow the strategy of extremely low debt/equity ratios like MSFT, with an average debt of a few hundred thousand to assets of millions. They know that adding more debt is always risky.

I do understand where the others are coming from… and yes, my view assumes that you aren’t going to invest crazily, and surely there’s no such thing as a guarantee in investing.

But, say you had a $1MM home, and had an 800K mortgage at a low 6.5% fixed rate. Now, someone gifts you 800K. Would you seriously pay off the entire 800K (assume no pre-payment penalties) now that you’re able? I personally don’t see why any rational investor would do so. While I might be totally wrong, I just don’t see why you would.

Let’s take it to an extreme, say that this mortgage was at 0%. For obvious reasons, you would not pay it off. You’d put the money in risk-free investments and win in the long-run.

What if it were at the rate of inflation? Same deal… there exist risk-free investments that give you a real return, since they take into account inflation.

Where do you draw the line? I certainly don’t advocate investing over paying off a mortgage if the rate was high… say 9%. But, at a rate in the mid-6′s, it probably works out for the better. Again, this assumes that you are not investing foolishly.

Regarding ROI and debt for companies… it might be a questionable statement, but I do believe that most finance books would argue for it rather than against it. That’s not to say that there are no exceptions.

Adding debt is always more risky… that’s why you need to make sure that you’re being compensated (more than) fairly for your risk to make it a worthwhile opportunity.

Just found this link by accident, but for those who might read the comments all the way:

Don’t follow the assumpitions and simplicity of the math described in the example above. For one it assumes “average annualized return of 9%”. That is AVERAGE return. Calculating returns using an average can lead to incorrect conclusions. The average annualized return of 9% doesn’t account for market fluctuations. For more information I suggest further exploring the topic “flaw of averages” or the “fallacy of averages”.

After doing so, you may understand that sticking your money in a money market account yeilding 4-5% is not only a safer bet, but more more likely to yield more money in the LONG RUN.

I am just out of college and a few years away from purchasing a house. With dropping rates I was wondering if there is any other way I could take advantage. For me the only possibility is student loans. I currently have a single loan (been consolidated already) at about 4.5%. Is there any way to refinance the loan at a lower rate? I would welcome any advice that could point me in the right direction. Thank you in advance!