Mortgage rate mathematics

Scripsit Colin Green

Um, have you calibrated your calculator recently? (1.0595^(1/365))-1 ought to be 0.00015836... - that is 0.0158% a day.

On the other hand the 0.482804% matches the *monthly* interest rate well.

This amount (less 4p) will be reached already on Jan 13th.

"Colin Green" wrote

Oh dear. Do you feel better now that you know better?

"Colin Green" wrote

No, the difference is because you were wrong!

"Colin Green" wrote

It may have been "obvious" to *you*, but that does not make it "correct" !

"Colin Green" wrote

... arguably correctly !!

"Colin Green" wrote

Not meaningless (it's 12 times the monthly rate) and not unorthodox.

"Colin Green" wrote

That'll be because the APR *is* the actual rate here!

"Colin Green" wrote

calculations!

You either need to get out more, or learn how banks calculate interest better!

"Colin Green" wrote

Eh?! ;-(

"Colin Green" wrote

Perhaps you should have asked them how they applied the rate, rather than simply assuming the incorrect way?

Sorry yeh I quoted the wrong figure there...

Hi,

Applying the daily rate 365 times gives £106,114.97 , Could you explain where the extra 13 days come from? Remember that although the interest payment is per month it is actually calculated per day and accumulated up to the point of the monthly payment.

Colin.

Well ok, but if you take an 'annual' rate of 5.95%, divide it by 12 and then apply that rate each month then the actual annual rate is 6.1%. So my point then is why quote the 5.95% rate at all? It is a property of the nuances of the calculation that is being used - and since the other nuances aren't directly published this could be construed as being misleading.

Not unorthodox to banks perhaps, but unorthodox from a mathematical perspective. The divide by 12 approach I would guess makes more sense if you pay interest annually, the annual interest payment is divided by 12 and the this in total corresponds to the toal interest for the year. But if you then actually use a monthly rate based on /12 and apply it each month then the effective rate is increased - due to compounding.

I re-iterate my main point, which is that the 5.95% figure is misleading. Also, I *did* just learn how banks calculate interest, and I question the technique used. That was the whole point of my post. As for the "getting out more" comment, well firstly pot kettle black, and secondly, if understanding how the single largest payment I make every month works is a waste of time then I don't know what isn't!

Indeed. But both approaches are easy to calculate, so why choose one that generates two percentage figures for the end user to digest?

Colin.

So you can work out the monthly interest charge on your mortgage. This can be quite useful at times.

Well ok, but if you take an 'annual' rate of 5.95%, divide it by 12 and then apply that rate each month then the actual annual rate is 6.1%. So my point then is why quote the 5.95% rate at all? It is a property of the nuances of the calculation that is being used - and since the other nuances aren't directly published this could be construed as being misleading.

Not unorthodox to banks perhaps, but unorthodox from a mathematical perspective. The divide by 12 approach I would guess makes more sense if you pay interest annually, the annual interest payment is divided by 12 and the this in total corresponds to the toal interest for the year. But if you then actually use a monthly rate based on /12 and apply it each month then the effective rate is increased - due to compounding.

I re-iterate my main point, which is that the 5.95% figure is misleading. Also, I *did* just learn how banks calculate interest, and I question the technique used. That was the whole point of my post. As for the "getting out more" comment, well firstly pot kettle black, and secondly, if understanding how the single largest payment I make every month works is a waste of time then I don't know what isn't!

Indeed. But both approaches are easy to calculate, so why choose one that generates two percentage figures for the end user to digest?

Colin.

Because it's traditional. But you're right, it would be more sensible to specify the rate as (5.95/12)% per month than as 5.95% per year.

But also because, if you make your monthly payments on your £100k loan (assuming for simplcity that it's interest-only), then over the course of each year it will cost you exactly £5950 of real money, not £6115.

No. It has nothing to do with nuances of calculation, but with "nuances" (if you want to call it that) of the charging mechanics. You get charged

A side-effect of this is that if you were to let the debt mount up by reducing your payment frequency from monthly to annually, then your £100k interest-only loan would cost you £6115 of real money per year.

That's the simple reason why both ways of specifying the rate make sense.

They *are* published, because the law forces them to state the APR. But the fact remains that the contract rate (in this case the 5.95% figure) forms the basis of the calculation of exactly how much interest is charged each month, the APR does not. They don't publish an APR and make a 12th-root calculation to work out how much to charge each month, but they publish a NAR (nominal annual rate) and make a divide-by-12 calculation instead, which is also easier.

On the contrary. If you paid interest annually, you wouldn't need to divide by 12 at all. You'd just pay £5950 in one lump sum, on the day before each anniversary of the loan advance.

Exactly. That's hardly unorthodox.

Tim can be a bit of a tease. Mustn't let him wind you up.

Because basically, even though the charging period is really the month and not the year, the rate is nevertheless quoted on an annual basis because it's traditional. If there were no compounding, there would be no difference, because a rate is a rate is a rate (unless they're mace).

If you drive your car at 60 miles per hour, that's a traditional way of stating your speed, but because you're unlikely to keep your speed constant for a whole hour, it makes more sense to say 1 mile per minute, and even that'd be pushing it, so 88 feet per second is really much more sensible, but sadly tradition has not favoured that approach, because we live in a world full of morons to whom subtle nuances mean nothing. Get your valium tablets in room 207, up the stairs, third door on the left.

"Colin Green" wrote

"Colin Green" wrote

Oh dear. I think he means Jan 13th of the original year - not the following one!

"Colin Green" wrote

Remember that you quoted the wrong rate for daily?! Well, 0.48% per day will take only 12 days (ie from Jan 1 to Jan 13).

"Colin Green" wrote

... which is what they quote as APR ...

"Colin Green" wrote

Because it makes it easy to work out the monthly interest amount - and lot's of people want to work out their monthly interest simply. They don't expect to take an "actual" annual rate, convert it to daily, decide how many days are in that particular month, apply the daily rate that many times, etc etc. Indeed most people would rather pay the same amount each month, rather than nearly 11% more in January than in February!

"Colin Green" wrote

But the APR *is* published - and if you didn't know why it was different, then you should have asked!

"Colin Green" wrote

What on earth is that meant to mean? Mathematically, *any* method is just as valid.

"Colin Green" wrote

It makes sense whichever way you want to do it.

"Colin Green" wrote

As everyone knows.

"Colin Green" wrote

Only if you make unwarranted assumptions!

"Colin Green" wrote

You want banks instead to use a daily rate? Why?

"Colin Green" wrote

In your first post you didn't come across as trying to understand it better; rather as preaching "look what I've found out!".

"Colin Green" wrote

Because some people prefer simple interest arithmetic - they can't get their heads around compound interest arithmetic. Anyway, haven't you noticed how all basic calculators never have a "to the power" function? Do you expect people to go out and buy a new scientific calculator just so you can have it your way??! :-(

Am I seeing double? ;-)

"Ronald Raygun" wrote

Ah, you've given the game away now. BTW, how are the bifocals?

Yes I can see that - if you pay the interest and thus don't generate any compounding.

Yes I see the distinction now. 5.95% is an actual interest rate, whereas

I meant to say: calculated annually - but paid monthly. So you would pay 1/12th of the annual interest each month.

Hey, you'll cause trouble with talk like that. Now get back in line before I zap you with the cattle prod :)

Colin

In message , Colin Green writes

No, its 5.95/365. Thius ACCRUES on a daily basis and COMPIOUNDS monthly

Youve lost me there completely.

Not if IF compound the 9imterest monthly, which is what i think they do.

Yes, some divide the monthly rate by the number of days in the month some divide by the number of days in the year.

No, its VERY important. Becuase from the basic rate, and the basis of the interest compound period, you can deduce the APR but from just an APR you cant figure out anything.

APR was devised by the Government, need I say more?

In message , Colin Green writes

Because that is the rate which is used to calculate how much interest you pay. The APR isnt.

Not so. APRs are a relatively recent innovation in the world of finance. Clearing banks, the BoE, Government and every financial institution you can think of including the Treasury, Discounters, Forfaiters, Bond Brokers etc., do it that way.

Thats right. IN fact many of the institutions I referred to above traditionally compounded quarterly.

Yeh but mostly folks want to work with a monthly rate and an annual rate, and you can get the former by simply taking the twelfth root of the latter.

ok, well I got there in the end, perhaps via a slightly more painful route than was necessary.

I was coming from the angle of there being only one 'proper' annual rate, and thus the only 'proper' monthly rate is the twelfth root [from that perspective]. I see the distinction now between an actual rate(5.95%) and an effective rate(6.1%) - that is different because of compounding.

Without this distinction in mind it seemed to me that the 5.95% was just a function of an arbitrarily choosen interest calculation (divide by

... but I get it now, I think.

Well ok, that wasn't intentional, but point taken. I guess I come from the George Bush school of diplomacy - attack first, ask questions later :)

YES!... at least once I've bought a job lot and put them on ebay (Bush school of economics).

Colin.

I've asked them, but they're not saying. I think that means they're OK because I'm sure they'd have complained otherwise.

If they were daft enough to throw away their log tables, then yes, they jolly well should. A basic calculator is OK for doing any interpolation which might be needed.

"Ronald Raygun" wrote

Didn't someone say it was the 21st century now? ;-)

Well, there's no "best before" date marked on mine, nor on my slide rule and typewriter.