# Interest Rates V APR



## Elcato (12 Dec 2001)

Can someone explain to me what is the difference between Interest Rates v APR ? - I'm a complete novice to this !


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## CM (13 Dec 2001)

It depends on the institution - as far as I know most (all?) banks calculate interest daily. I think that Building societies traditionally calculated interest annually but most have moved to monthly or daily calculation of interest now. Irish Nationwide is the only institution which still calculates interest annually as far as I know - at least they were still doing this up to a year ago. The excuse they offered at the time was that their computer systems had not yet been reprogrammed to do otherwise. :rolleyes  EBS moved from annual to monthly calculation of interest in the last few years. If you are in doubt ask and persist even if your query is initially met with blank stares or you are offered the same explanation that the EBS gave a friend of mine - "it's a big complicated formula". :lol


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## Emma (13 Dec 2001)

CM,

I'm sorry if I sound stupid  , but why do they mention APR if they calculate it on the interest rate?.  I can't get my head around this.


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## CM (13 Dec 2001)

*APR*

I'm not sure how to make this any clearer! Forget about nominal rates and concentrate on the quoted APR which represents the true cost of a loan (in the case of deposits ignore the nominal rate and concentrate on the CAR - Compound Annual Rate). 

As an example, in general a nominal rate with interest calculated annually will result in higher APR than if the same nominal rate is used but the interest calculated monthly or daily. Other factors and charges are also taken into account when calculating the APR such that APR reflects the true cost of a loan and is a figure which can be used to compare loans on a like for like basis. Comparing nominal rates in this way is meaningless.

Does this make any more sense...?


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## Sarah Wellband (13 Dec 2001)

*Re: APR*

The best way to compare lenders is to ignore the APR and the interest rate and look at the cost per thousand (CPT). Multiple this by the mortgage amount for the exact monthly payment. For example £150,000 over 25 years at 3.55% (EBS discounted variable rate) gives a CPT of 5.03. 150 x 5.03 = £754.50 per month. All lenders publish their CPT's for their rates on their websites; finfacts also quote CPT's over 20 years for all lenders.


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## Emma (13 Dec 2001)

Sarah,

Thanks, unfortunately I'm not in this business & I find it hard to understand the jargon, obviously comes easier to others.  How did you get 5.03, maybe you could explain the calculation to me ?

Tks,
Emma


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## CM (13 Dec 2001)

*APR*

Sarah - there was a  about the pros and cons of using CPT versus APR when comparing loans. I tend to lean towards CPT but Brendan seems to prefer APR. Anyway - your example is fine except that you use the one year discounted rate which we all know is <!--EZCODE ITALIC START-->_ not_<!--EZCODE ITALIC END--> a good indication of the normal cost in the longer term. Better to use the standard variable CPT and treat the one year discount savings as the once off bonus that it is.

Emma - don't worry, stuff like this is not obvious - apologies if I made it sound like it is! I'm not an industry insider/professional and only learnt about stuff like this through practice.


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## Sarah Wellband (14 Dec 2001)

Unfortunately not, Emma. We are supplied with new CTP sheets as and when interest rates change and work from them. One lender I just spoke to said they just feed the new interest rate into their computer. The actual formula for calcuating the APR is laid down in the 1995 Consumer Credit Act but is horribly complex.


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## Sarah Wellband (14 Dec 2001)

Point taken CM - std. variable rate 4.6% or £769.50 on £150k over 30 years. OK?


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## CM (14 Dec 2001)

*Pedantic me*

Fair enough Sarah. Just to clarify (to Emma) the cost per thousand figure depends on the mortgage term so the example quoted by Sarah will <!--EZCODE ITALIC START-->_ only_<!--EZCODE ITALIC END--> work for a 30 year term. The relevant CPT figures for the arguably more common case of a 20 year term are available from Finfacts.

Is this making a bit more sense or are we confusing you completely at this stage!


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## Emma (14 Dec 2001)

CM/Sarah,

No it does make more sense  I think I've got a better handle on it now, but I'd love to know how they work out the CPT figure!.  Would you recommend going for a 20/25/30 year mortgage ?

Tks,
Emma


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## CM (14 Dec 2001)

*Mortgage term*

Didn't I tell you it was a "big complicated formula"! :lol  Seriously, perhaps somebody (Liam perhaps?) could explain the mechanics of the CPT and/or APR calculations?

As regards mortgage term the shorter the better! The longer the mortgage runs the more interest you pay. Karl Jeacle's mortgage calculator (instructions here) is great for illustrating how different variables (including term) affect total mortgage cost. There's no harm in starting with, say, a 20 year term and then making "accelerated repayments" (e.g. foregoing rate reductions and leaving your repayment above what would normally be charged and/or making lump sum capital repayments whenever possible) in order to reduce the effective term as you go. This is possible without penalty with most annuity/repayment mortgages other than fixed rate mortgages which normally charge penalties/fees for breaking the fixed rate agreement and/or early redemption.

There's more on this and related topics in the  and elsewhere on AAM and the archives.


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## Liam D Ferguson (14 Dec 2001)

*Re: Mortgage term*

Hi Emma & CM, 

I hate to disappoint you but I don't actually know the mathematical formula for working out CPT or APR.   

I cheat - I have a piece of software installed on my PC - I can input a mortgage amount, term and rate and it will spit back the repayments and other relevant bits of info.  

Emma - I am in absolute agreement with CM on the "shorter the better" principle.  A longer-term mortgage will  have lower monthly repayments but will cost more over the longer term.  Set your mortgage term as short as you can comfortably afford the monthly repayments.  

Regards, 

Liam D Ferguson
www.ferga.com


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## Observer (15 Dec 2001)

*APR and all that*

The APR concept is relatively simple. Start with the basics: an APR of 10% means if I borrow £100, I repay exactly £110 exactly one year later.   Thats why they call it ANNUAL PERCENTAGE RATE!

Now lets look at rates over other periods.  Suppose I have a £100 overdraft at the start of year at an APR of 10%.  In theory, if I make no other transactions on the a/c (inc fees charges etc.) I should owe exactly £110 at years end.  How is this done if interest is charged, say, quarterly?  Well, its not simply a question of paying 2.5% interest per quarter.  Why?  Because in quarter 2 I'd end up paying interest on £100 + £2.50 (total interest for the quarter being £2.5625, in quarter 3 I pay interest on £100 +£2.5625 + £2.50 etc. 

To get the true quarterly rate I must convert the interest rate to the format 1+i where i is the decimal equivalent of the APR.  In this case APR =10% = 0.1 so my 1+i format = 1.1  (which is the number I must multiply the year start debt by to get the year end debt.)  Then get the fourth root of 1.1 (or the square root of the square root of 1.1) to get the 1+i factor for one fourth of a year. This is 1.024113589....   Therefore the true interest rate per quarter is 2.4113689%

You can check this as follows:
Quarter  Opening balance Interest      Closing Balance
1          100                   2.411359    102.411359
2          102.411359        2.469505     104.880864
3          104.880864        2.529054     107.409918
4          107.409918        2.590039     109.999957 

Correct apart from rounding errors; all figures shown to 6 decimal places.  


Similarly the true daily rate is (the 365th root of 1+i) -1 
In this case this is (the 365th root of 1.1) - 1
=  1.000261158 - 1  
= .000261158  
= .0261158% per day.

The Excel formula for 365th root of 1.1 is =1.1^(1/365)


Lesson 2 is how to calculate the APR when you know the repayments.  Thats for honours students!


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## CM (15 Dec 2001)

*APR*

Do you know how "other charges" are also factored into the APR calculation? Is it simply a case of any regular charges of £x per month or up-front charges of £y being worked into the equations?


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## Observer (19 Dec 2001)

*More APR*

Basically, yes.  Charges are treated just as extra repayments and accounted for accordingly.


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## Liam D Ferguson (19 Dec 2001)

*Re: More APR*

Hi Observer, 

This is most interesting.  Your definition of APR suggests that it takes account of charges, fees and frequency of calculation of interest.  That's good.  

But it does not and cannot account for future changes in fees or margin.  Many (most) lenders have recently proved that they are not averse to increasing their margin on a loan when they can comfortably get away with it (like when rates are dropping so consumers aren't complaining).  Such practices would obviously not have been reflected in the APR's quoted at the point of sale.  That's bad.   

My point is that, while it's been said here on AAM that APRs are the only true way to compare mortgage and other loan products, I would say that it should not be relied on too heavily as it is as flawed as the rest and that consumers should look at a number of factors <!--EZCODE ITALIC START-->_ not just APR_<!--EZCODE ITALIC END-->.

Regards, 

Liam D Ferguson
www.ferga.com


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## CM (19 Dec 2001)

*APR*

Yes - it's worth noting that the APR represents the true cost of the loan <!--EZCODE ITALIC START-->_ at that specific point in time_<!--EZCODE ITALIC END-->. It is impossible to predict what way rates and margins (other than with trackers with a built-in maximum margin guarantee) will go in the future. 

What additional factors did you have in mind Liam? Past "performance" on margins would be one I presume?


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## Liam D Ferguson (19 Dec 2001)

*Re: APR*

Yes that's a very important one.  Also track record on speed of passing on rate changes.  And then issues appropriate to an individual's particular requirements such as flexibility of product to accept lump sum repayments, increased monthly repayments, payment holidays etc.  If one is choosing a fixed rate, the lender's formula for calculating breakage penalties (although again this is "point in time" as most lenders allow themselves discretion on calculation of such penalties.


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## Observer (23 Dec 2001)

*APR*

Liam,

Fair point. Obviously APR can change and if it does, then this must be considered as an other factor.  But apart from cost, which APR (at any given point in time) is a true reflection of, I don't really see any other hugely significant factors.  There are minor things such as policies on arrears, ease of remortgaging etc., but basically, its a commodity product and cost is king.

This is even more so with the tracker mortgage, where APR is essentially defined (if not fixed!) over the entire life of the mortgage.

Now if institutions started to offer really innovative stuff like current account mortgages, then the picture would change.  But, I don't see any evidence of this happening............

Perhaps Liam could comment on the demand, if any, for this?


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## CM (23 Dec 2001)

*"Current account" mortgages*

For there to be a significant demand for such products I reckon that a prerequisite is that most individuals understand the mechanics of mortgage products better than they do now in order to appreciate the advantages of "current account" mortgages, tracker mortgages etc. For a variety of reasons, I don't believe that this is the case today. Hopefully, as consumers become more educated in this field demand for better value and more equitable products will increase and the financial institutions will cater for this demand.


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## Liam D Ferguson (24 Dec 2001)

*Re: "Current account" mortgages*

Hi Observer, 

I'd love to see Current Account mortgages here.  However, I'm not optimistic that they're on their way here anytime soon.  CM makes a very valid point - the target market must understand and appreciate the benefits of such flexibility for it to sell in big numbers.  

I'm guessing here but I'd imagine that a current account mortgage requires a fairly advanced IT system to back it up.  So there's an expense unless some lender wants to use a UK system.  

If I was a lender, I'd think long and hard before committing substantial resources to launch a mortgage product into a market which (a) is small, (b) provides the Irish Nationwide with plenty of residential mortgage business despite the fact that they calculate interest annually and add rate loadings in unusual circumstances,  and yet (c) doesn't provide Tusa with enough business to survive despite the fact that they had some excellent rates.  

Liam D Ferguson
www.ferga.com


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## adrian (13 Oct 2003)

*Comaring APR's and CPT*

Just been comparing interest rates at:

www.finfacts.com/Private/...rt_var.htm

I am still uncertain about a couple of things:

Let's look at the cheapest variable rate APR that's quoted, AIB Stand'd Var'ble at 3.3% this works out at a CPT of €5.69 

Now, look at First Active 6mth Dis Var, APR 3.5% (higher than AIB) but the lowest CPT of €531.00

Okay, now how can a lower APR mean a higher CPT over 20 years? Based on the APR explanation as ANNUAL PERCENTAGE RATE in this forum, it just doesn't make sense to me. What is making the difference? 

Also Permanent TSB's one year fixed rate new business looks fairly competitive at a CPT of €5.34, but again APR is currently higher (3.5%) than AIB. So why is it that you always hear that "AIB has the cheapest rate on the market"???

www.finfacts.com/Private/...rt_1yr.htm


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## BG (13 Oct 2003)

*> Comaring APR's and CPT*

adrian,
Your question is an excellent one and highlights the reason why it is important to look at all comparitive rates in addition to looking at other policies of any given lender, as Liam said earlier.
To look at your example: The CPT is based on the advertised rate.  The APR must take into account what the cost will be over the Lifetime of the mortgage.  This means factoring in all known costs at the time of quoting the APR. So in the case of Permanent tsb and First Active products you have quoted the APR works out the cost of borrowing during the initial 'discounted period' and after the discounted period where the loan reverts back to the Standard Variable Rate.  The APR will also factor in 'set-up' or 'redemption charges', if any.
The APR is the Cost of Credit and is for comparitive purposes.  The CPT is to help you work out what your monthly payments will be. APR and CPT are not comparible in themselves but, in a comparison such as the one you outlined, questions should be raised as to comparing other cost factors which a lender may have.  This would be further highlighted in all loans if ALL loans had to have Payment Protection Insurance and where different lenders charged different premia, again the APR would highlight this while the Cost Per Thousand  would not change.  As it currently stands Insurance Premia is not taken into account when calculating the APR. Nor are penalty charges for being in arrears.
The EU are currently considering introducing a 3rd Cost/Interest Indicator. This will give us better information and/or more confusion! Depending on your viewpoint.

BG


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## adrian (13 Oct 2003)

*Comparing APR's and CPT*

Thanks BG

I contacted Permanent TSB who explained that the CTP quoted only applied for the first year. After that it depends on the rate. Here's what they said when I asked a question about their CTP figure for a 1 yr fixed rate discount over 25 yrs:

"Thank you for your recent email. The figure quoted related to our 1 year
fixed discounted rate. It would depend after that year, what our rates our.
If you choose to go on this rate, you will receive correspondence after the
1st year of your mortgage and you will be given a breakdown of what our
rates are at that time. You then choose from this as to what rate you wish
to avail of."

To be honest, when talking about CPT I think that it's a little misleading when they don't explicitly say this when quoting on websites etc. My take on this is not to use CPT to compare mortgage products, when one of the products is a discount type product.


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## Marion (12 Mar 2004)

*Simpe explanation of APR*

This explanation was posted by *burgessbrendan* elsewhere:



APR is the true rate of interest on a loan. 

If you borrow €100 and pay €12 interest at the end of the year, the APR is 12%.

Example
You borrow €100,000 from a bank.
The rate of interest is 3% calculated monthly. 
3% is €3000
One month’s interest is €250 ( 3000/12)
At the end of January you will owe €100,250
In February, you will be charged interest on the €250 as well as on the €100,000.
So February’s interest is €250.625 

At the end of the year, you will owe €3040 interest so the APR is 3.04%
If the interest is calculated daily instead of monthly, you will owe €3045 interest. 

With interest rates at 3%, there is very little difference between flat rates and APR. And it doesn’t matter much if they charge it daily or monthly.

But a 10% flat rate charged monthly is 10.47% and 10.5% if charged daily. 

Why do lenders with the same APRs have different cost per thousand?
The APR must also include any charges which the lender imposes, so there may be additional charges. Of course, one lender might be miscalculating the APR.

Another thing to watch out for is term of the loan. A 30 year loan at 3% will have a lower cost per thousand as a 20 year loan at 3%. 

So should I focus on cost per thousand?
No. Consider both. 

The cost per thousand will tell you what your repayments will be in hard cash every month. This will vary depending on the term of the loan. As the cost per thousand includes an element of capital repayment, it is not the true “cost”. The true cost is the interest element. 

The APR will tell you the true cost and will allow you compare loans over different terms.


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