## [Housing Market Myths] Low Interest Rates Means I Pay Less

Posted by Lex Fear on June 2, 2007

This Post Is Rated: M for Midly Offensive. Discussion of house prices which may cause home-owners to scoff or worry. Some people my be offended by my accusations.

Previously: Prelude, House Prices Always Rise

In the previous Housing Market Myths post, I presented facts, figures and observations proving that house prices do not always rise, and in fact overall house prices rise in cycles or peaks and troughs as it were.

I am now going to demonstrate practically why low interest rates have been bad for the economy, home owners and naive or amateur investors.

The last property crash in the UK saw interest rates rise to record levels of up to 15.40% (1 Mar 1990 – AWD Moneyextra). Despite many bankruptcies and repossessions, high rate was nothing new. Just has house prices have always spectacularly risen and spectacularly fallen, so have interest rates in the UK:

- 5.50% 2007
- 3.50% 2003
- 6.00% 2000
- 5.13% 1994
- 14.88% 1989
- 7.38% 1988
- 13.88% 1985
- 8.05% 1984
- 15.13% 1981
- 5.00% 1977
- 15% 1976
- 9.75% 1975
- Source: Bank of England

UK Interest rates, as can plainly be seen, hit their low in 2003, anyone who bought in 2003 at the bottom will be feeling the heat of a 2.0% rise (over 50% increase in their interest payments) more than recent lemmings buyers. Not only that, the future does not look good according to recent news reports.

Regardless of whether the rates rise or not, it is important to realise the effects of low interest rates on the economy and especially on the psychology on average potential house buyers. I’m going to start by making an arrogant but informed blanket statement about people in the UK:

British people are absolutely crap at maths.

I say this because, if they were any good, we would not have the current situation where even key workers struggle to buy housing made for key workers let alone the rest of the population. The problem is the perception in the public and the media: low interest rate good, high interest rate bad.

Low Interest Rate, Good?

It’s easy to see where this perception comes from. If you’re going to take out a loan for £300,000 for 25 years at a rate of 5% then your monthly payment is going to be lower than the same deal at a 10% rate of interest. People see low rates, then they think to themselves “I can afford this”, so what happens is everyone rushes to get this loan. Thus the market is actually pushed up, as the stock gets lower, the prices go up.

This kind of bubble can be corrected easily: by raising interest rates, making the loans less attractive, which in turn lowers the price of the stock as demand falls.

Unfortunately, this is where the UK government (and specifically the current Chancellor of the Exchequer: Gordon Brown) and the MPC, have done recent homeowners a great injustice. Instead of taking control of house prices by raising interest rates before the prices went astronomical, Gordon pressed ahead with his unachievable 2% target and they continued to try and keep the base rate low. As more sheeple took advantage disadvantage of the lower rates, prices continued to spiral upwards, and more people were priced out. Those who have stretched themselves to the limit in borrowing leave themselves vulnerable to very small rate changes. As the interest rate creeps up half a percentage, they start to find themselves struggling to meet bills and basic necessities, until they bail out by declaring bankruptcy.

Low interest rates are not only bad for increasing the risk and level of personal debt, they are bad for savers. So even people who are financially astute are punished because they get little reward for their hard work.

Finally low interest rates and increasingly larger loan amounts have had a detrimental effect on Britain’s industries at home. More and more people have had to tighten their belts, which has meant that shopping has significantly lost appeal and supermarkets are reduced to selling crap whilst killing UK agriculture at the same time.

High Interest Rate, Bad?

It’s pretty clear that if interest rates ever hit 15% again, that many people are going to find themselves in a lot of trouble. But there are a number of groups that will benefit including:

- Seasoned property investors (who will be able to buy at rock bottom prices)
- Tenants (Who can still choose where to live, and can rent from the group above)
- Savers (Those who have more in equity than they have in debt)
- First time buyers (buying at rock bottom of the cycle)
- Commercial industry (customers are be able to afford quality and luxury goods again)
- Employees (higher wage increases)

Higher interest rates discourage borrowing and encourage saving. If less people are taking out mortgages, less people are seeking to buy housing. All it will take is a bit of seller panic to set in and it will drop like sack of potatoes. Even if sellers hold on, the market will stagnate before dropping more slowly whilst waiting for wages to catch up.

*This is the maths part…*

This section edited in red, thanks Emily (comments)!

Let’s imagine a house that is worth £300,000 at present.

- You take out a 100% mortgage at a rate of 6% over 25 years
- This gives you a monthly payment of Â£1,956.00
- The total cost of your house is: £1956 * (12 * 25) = £586,800 (a 97% increase of original price)!

Now let’s imagine interest rates rise to 15%, bringing the value of the same property down to £100,000. If you took out the same 25 year deal your costs would be:

- £100,000 at 15% for 25 years
- Monthly payment of £1289.00
- Total cost of your house: £1289 * (12 * 25) = £386,700 (a 287% increase BUT almost £200,000 less than the same property bought at £300k at 6% interest)!

Since you know you can afford the original £2000 monthly payment, we can actually lower the term for repayment of the original mortgage (which should be the objective, low house prices, smaller mortgages):

- £100,000 at 15% for 10 years
- Monthly payment of £1660
- Total cost of your house: £1660 * (12 * 10) = £199,200!

Therefore high interest rates actually prevent growth in borrowing, create affordable housing and allow people to either pay off their mortgages faster and/or lower the rate of their monthly payments.

With lower monthly payments you have more room to maneuver around interest rate hikes, or with a smaller term, the effects of a rate hike are not going to be long term. It is also far easier to pay off £100k at a high interest rate than £300k at a low one, with high interest your money also goes to further and if rates then fall you are also going to do even better. (However if rate falls lead to high inflation it will take a while for your wages to catch up, in that time price of goods and services increases and you find the power of your money limited.)

So why doesn’t this happen in the real world? Herd mentality is one explanation. Back in the late 90’s/early 00’s everyone was beginning to learn how investors make money from property and wanted a go at it themselves. The problem is they didn’t know the first rule of investing.

The result was that many buy-to-let’ers found they had to reduce their rental rates to compete with the flood of rental properties on the market. At the same time, many newbies who bought a ridiculously priced property found that the rent was not enough to cover their mortgage repayments. The real winners are those that have sold to rent or who have been in the game a long time.

What happens next?

Many will quote that overused byline that the government won’t let it happen. Well guess what? The government (Gordon Brown) turned over control of interest rates to the MPC 10 years ago. This means that if things get out of control, the MPC will be used as the scapegoat. There is nothing to suggest in history that governments have been able to control inflation and there is nothing to suggest that they can control it now. The only tool that they have, outside of introducing new regulations to cap prices or forcing home-owners to lower their prices, is the base rate, which they can either lower or raise.

EDIT: Thanks Ian (comments)

If everyone learned this basic economic principle then sellers would be forced to haggle instead of taking advantage of naive buyers. The housing market would probably regulate itself invisibly capping prices, since buyers would actually walk away from overpriced deals. It also helps if buyers tool themselves up before going out looking for a property.

Take my advice, look out for lower rents, be prepared to rent for a while and wait for interest rates to rise and prices to fall before committing to a mortgage which will leave you with negative equity.

Read: Myth: House Prices Always Rise

Coming Soon: Housing Market Lies: Your Home Is An Investment

## Ian said

You can’t accuse the British public of being crap at maths, and then get basic English wrong! It’s “basic economic principle”, not “principal”.

## Lex Fear said

OK Ian, you got me there, spell-check error.

You don’t have to believe this but in my job I have to type “principal” 4-5 times a day so it was a genuine mistake.

However, my spelling error doesn’t negate the fact that the British public are crap at maths, all it proves is I

maybe bad at spelling.Do I take it I got everything else right?

## Emily said

While I agree people are deluding themselves about houses being a great investment right now, your Maths demonstration is misleading. Adding up a string of payments made at different dates in the future and treating them all as ‘pounds today’ is just wrong. Time value of money and all that.

Good point badly made.

## Lex Fear said

Emily,

Thanks for your comment, your thoughts are welcome.

I may need to point out though that I have not simply ‘added up’ a string of payments. These are monthly payments inc. compound interest calculated on the loan amount. Unless, at some point during the loan term the loan is paid off, these are the correct calculations for a fixed term payable monthly.

Admittedly I used a spreadsheet I downloaded to make my task easier but if you wanted to test it with the mathematical formula here is an example.

A = £300,000

i = 6.00%/12 = 0.0050%

N = 12*25 = 300

n = 0

P = iA / [1 – (1+i)^-N] = 1932.904 (slightly off from the automated spreadsheet)

1932.90 * 300 = £579,870

As for “pounds today”, I think I explained this when I explained how high vs low interest rates work!

Value of money is affected directly by inflation. High interest rates means high annual wage increases (excluding bonuses et al). Higher wages ‘eat away’ at the cost of your debt. In contrast, low inflation means lower wage increases, ie, you have less chance of paying the loan off sooner and you will continue to feel the cost of your monthly loan payments.

If you have some evidence to the contrary or feel I’ve missed any important calculations- feel free to respond.

## Anonymous said

Hi Alex,

You say I have not simply ‘added up’ a string of payments. Yet consider total cost of your house is: £1956 * (12 * 25) = £586,800. As we all learned in primary school, multiplying is simply a quick way of adding together lots of identical numbers, eg 3×4 = 4+4+4. You’ve added 300 lots of £1956.

The reason why it’s wrong to add them up is because each payment of £1956 is worth a different amount in today’s money due to inflation eroding its purchasing power. A pound will still be a pound in 25 years (unless it’s a Euro) but you won’t be able to buy as much with it, just as 25 years ago you could buy 10 Mars Bars for a pound, now you get 2 with a bit of change. Imagine yourself back in 1982. You agree to pay your child 10p a month pocket money for the next 25 years. Great, they think, a Mars a month for 25 years: £30 or 300 Mars bars. But then you test their reasoning skills: would they rather that or 25p a month for 10 years? Using your calculation method the two options are identical. But if they’d picked the first, in 300 months they’d have been able to buy only 154 Mars bars (assuming a constant rate of Mars bar inflation), by the end having to wait over four months to buy one. With the second they’d have been able to buy 225 in just 120 months. Certainly not identical outcomes. Your child, receiving the sums, would surely prefer the 10 year option. You, making the payments, would equally surely have preferred the 25 year option. So it is both nonsensical and misleading to use the total figure arrived at by summing all future payments to decide which mortgage is better value for the borrower.

If you don’t believe that, can I offer you a win-win contract? You give me £10,000 today and I’ll give you £15,000 in 25 years time. If a pound today is worth the same as a pound in 25 years, you gain £5,000 or 50% (though by your method, it’d be 33% but more on that in a minute). I’m sufficiently confident that I can earn more than 1.6%pa in the intervening period that I also believe I’ll gain. How about it?

You ask if you’ve missed any important calculation so since there was a discussion about the poor state of Maths, perhaps it needs to be said that percentage change calculates how much a number changes from its initial value, ie change in value divided by start value. You state that £586,800 is a 49% increase on £300,000. £600,000 is 100% greater than £300,000 so a basic check would tell you the answer the spreadsheet gave was wrong. The quick method used in spreadsheets (because it doesn’t require brackets!) is not intuitive because it’s an algebraic equivalent: end value divided by start value minus 1. You have used 1 minus start value over end value, in other words, change in value divided by end value. Whoops!

## Lex Fear said

Hello again Emily,

Thanks for pointing out another error that I have made (not the spreadsheet calculation- I added the percentage increases myself- doh!)

It was late at night, it was rushed- Here’s what I did wrong. After calculating the total sum I went for the percentage increase (to add a bit of gloss on the top) and did this:

300k/586.8k = 51%

What I should have done is:

(586.8k – 300k)/300k = 97% increase.

I have no problem admitting that error- as I said it was mine not the automated spreadsheet- I have now corrected this in the post.

However, if you doubt the spreadsheet method, then I posted the formula in my 1st response to you.

The formula is correct, the bank will always calculate the whole amount including interest outstanding to determine the monthly payment (obviously the examples need to be based on a fixed rate of inflation to start with, but as inflation changes the formula can be recalculated). The bank do this because they are the ones immediately out of pocket by £300,000.

I don’t know where you got:

“end value divided by start value minus 1. You have used 1 minus start value over end value, in other words, change in value divided by end value.”

I didn’t know the end value until I calculated interest and monthly payments.

I really appreciate the time you’ve taken to comment but could you please try to post formulas correctly so that I’m able to work out what you mean?

If you took 1 month off the term eg. 299, then you still end up with a calculation of 1923.225 (Again a slight difference of £10 because we’re working with decimal fractions).

You are still going on about the value of money over time. OK let’s go with the mars bar example.

You are correct that a Mars Bar would cost much less 25 years ago than it would today. You are also correct that if offered the deal between 10px25 years or 25px10 years obviously you would choose the latter!

You correctly factored in inflation on the Mars Bar…

BUT! you missed on vital calculation- inflation in wages. What person would join a company and agree to a 10-25 year contract being paid the same rate each month/year.

So for your model to be a realistic representation, your pocket money should also increase with inflation.

Now here’s the crunch.

So let’s say your pocket money is 10p per month at an inflation rate of 6% p/annum (0.5% p/month).

Each month then, your pocket money increases by 0.005, however if you spend it all on mars bars, you never really gain any capital.

If mars bars increase at the same rate of inflation, all well and good, you will be kept in mars bars for the full term of the pocket money contract.

If mars bar inflation goes down, whilst your pocket money remains steady, then after saving up all those 0.005 increases you may be able to buy an extra mars bar and become a mars bar investor.

But what if the price of mars bars rises above pocket money inflation? Pretty soon, you are unable to buy one every month, you have to wait and save longer.

Now let’s apply this to mortgages. Most banks offer fixed and variable rates set at 1-2% higher than the base rate of inflation. If they didn’t do this they would not make any profit (outside of their penalty charges scheme-but thats for another post).

So we have these factors in play:

House Price

Mortgage

Wages

This would represent the typical home owner.

Let’s say the base rate is set to 5.5%, your wages will increase by 5.5% this year (if your employer is honest). The bank sets your variable mortgage to 6.5%

Wages = 5.5% Inflation

Mortgage = 6.5% Inflation

So the mortgage rate is always going to be higher than the wage increase. Therefore the deciding factor is your house price.

You house price is based on what a FTB can afford to pay. So house prices are capped to say 3-5 times salary.

If house prices rise above affordability, wages need to catch up as I’ve already explained. So your house value stagnates or drops, your mortgage rises (as the bank passes on the rate increase) and your wages increase (but at a lower rate than the mortgage).

The only person who sees a benefit from this is the buyer, who’s wage is catching up with the 3-5x ratio and is able to take out a smaller or relative size mortgage (due to lower/relative house prices) and pay it off sooner or reduce the size of monthly payments.

So may I make a counter offer?

I give you £10,000 today to buy 300000 mars bars (£30 each I know- they’re overpriced btw), you pay me back over 25 years at a variable rate starting at 6% and I’ll pass on any rates increases. If it gets to 15% and you can’t afford the monthly payments anymore, you can sell your mars bars to the next person who will offer you £6000 (since they would have to take out the loan at 15% rather than the attractive rate of 6% you got).

Depending on how much you have already paid me back, you may just be able to balance the amount, or end up in negative equity.

Also, can I ask when you are commenting to break up your paragraphs and calculations so it is easier to read. I fear we may lose people who aren’t so good at this, and the whole idea of my post is to enlighten people who would not normally consider this.

Thanks.

## Emily said

Hiya,

Sorry the paragraphs looked so dense – pasted without checking layout.

On the % calc algebra, I used long hand to avoid an offputting array of x’s when making general statements but that was a mistake.

Calc for % change

= (x2 – x1)/x1

= x2/x1 – x1/x1

= x2/x1 – 1 (the quick but non-intuitive method).

That’s where the ‘minus 1′ comes from (not the number of months).

Your original latenight calc was (586.8 – 300)/586.8, or in general terms (x2 – x1)/x2

= 286.8/586.8 = 49%.

I used the pocket money example to try to show why summing a string of payments through time doesn’t give a meaningful result. It’s interesting that you’re so sure you’d choose the 25p for 10 years option when both alternatives sum to £30. If the method gave useful information you should be indifferent between them.

As I said at the start, I agree with the thrust of your argument, the details just need some tidying up!

The market’s certainly not expecting prices to fall by the 67% you use in your example but then, nor were the Japanese. “In Japan’s six largest cities, residential prices dropped 64% between 1991 and 2004. By most estimates, millions of homebuyers suffered substantial losses on the single largest purchase of their lives.” according to home.co.uk.

Ugly, except as you say, for those waiting on the sideline with cash in hand.

Timing’s the tricky part!

## Lex Fear said

Ha ha, agreed!

Thanks for taking the time to post Emily.

I may have got away with some sloppy figures for a moment (which was the opposite of my whole intention)!

I’m glad you had the tenacity to keep coming back.

Of course you’re right about the 25px10 years, but then my point was I’d take that 25p and stick it in a high interest ISA, as I’m sure you would. Whereas 10p installments gives less return on your interest… It’s all about interest.

Yes 67% is a little hard to believe isn’t it, but as you prove, not an impossibility (Did you go to my last myths post and watch the video there? Great fun).

Currently my expectations are a drop of 30-40%, but then some areas will fare better than others. My expectations may change depending on what happens next.

I take it since you also post late at night you’re a student (studying some form of maths degree)? However this is a Saturday night so perhaps you’re beyond your student days?

It’s been 4 years since I studied Management Science so you certainly gave me a workout.