Annual interest rate v. APR

W

WhiteCoat

Registered User
Messages
94
Please be gentle!

I'm reviewing a mortgage. The interest rate per original letter of offer is 4.75% and the APR is 4.9%.

My understanding is that if there are no other charges, the APR would equal the interest rate. Is this correct?

As a follow-on, what charges are/were typically included by banks causing the higher APR? (i.e. I'm not aware of any arrangement or other fees).

Any guidance appreciated!
 
WhiteCoat said:
My understanding is that if there are no other charges, the APR would equal the interest rate. Is this correct?
Click to expand...

No.

The easiest way to explain it is with an interest rate of 12% which is 1% per month.

Borrow €1,000.

At the end of the first month, your balance is €1,010 (€1,000 +1%)
At the end of the second month your balance is €1,020.10 (€1010 +1%)
If you paid nothing at all for the year, your balance at the end would be €1,126.80

So the APR is 12.68%.

With a mortgage rate of 4.75%, it doesn't make that much difference.

Brendan
 
The apr allows for the effect of compounding. Interest compounding at a greater frequency than annual (usually monthly) will show a higher apr than the quoted interest rate. It shows the real effect of the interest rate.

In the example you show interest seems to be charged monthly ie (1 + 0.0475/12)^12 = 1.0485 or 4.9% rounded up.
 
Thanks Brendan and Zebedee.

WhiteCoat said:
My understanding is that if there are no other charges, the APR would equal the interest rate. Is this correct?
Click to expand...

The reason that I wrote this is that it what was said from a seemingly authoritative source but I fully accept your correction. Makes more sense. Thanks. Much appreciated.
 
I simplified it a bit to get at the core of the issue.

I understand that charges must also be factored in, but they are not common in Ireland.

If fact, when it comes to mortgages, the opposite is the case. Cash back is not factored in, if I understand it correctly.

Brendan
 
Thanks RedOnion,

Indeed, it was a US site. But your question got me thinking again. Somewhere in the deep recesses, I had the idea that the calc was not quite as simple as set out above (although what's set out is a very good approximation and answers my main question).

Because of the time of the loan under review, I believe the relevant EU directive for the APR calc is 98/7/EC...…...the maths here is now a little beyond my pay grade, alas. Perhaps someone can explain it in layman's speak...….it would probably be of general interest.
 
@WhiteCoat
The US version ignores compounding effect.

Unusually, Wikipedia covers it well. You discount all your future cash flows such that your present value of repayments equals the loan amount, and the discount rate used is the APR.

https://en.m.wikipedia.org/wiki/Annual_percentage_rate

I think the main change since your example is a change from APR to APRC for mortgages.

There are 'funny' things with fixed rate mortgages, that in my view make it meaningless. To calculate APR the lender assumes that it reverts to SVR at the end of fixed period. So if you look at UB 2 year fixed rate of 2.3%, the APR is 3.9%. but with AIB, their 2 year fixed rate of 3.2% has an APR if 3.23%
 
@WhiteCoat I'll give it a crack and hopefully avoid getting in too deep!

The APR reflects the total cost of credit expressed as an annual percentage rate, hence the name, allowing you to compare finance offers with potentially different characteristics.

The beauty of the APR for comparison purposes is you do not need to know the lender's effective interest rate, the interval of interest compounding e.g. monthly repayments with quarterly compounding, the day count convention used to measure time intervals between cash flows, etc. used in the original calculation. It is all irrelevant;

All you do need to know to compute an APR are the value and dates of the credit agreement cash flows (the amount/s advanced and repayments), and the day count convention to apply, which determines the method used in computing the time interval between each cash flow and the initial draw down (first amount advanced), expressed as a fraction of a whole year.

If you are familiar with the Microsoft Excel XIRR function you can compute an APR the way everyone else seems to do outside the European Union. That is you define the cash flow dates and values, and internally Excel determines the XIRR result using time intervals computed using the Actual/365 day count convention (https://en.wikipedia.org/wiki/Day_count_convention#Actual/365_Fixed).

In the EU, the directive you refer to defines yet a different method for computing time intervals, which is why the Excel XIRR may not produce the exact the same result as the EU APR formula (it does for most straightforward calculations though). Without getting bogged down too much in the details, time intervals are defined in whole weeks, months or years (determined by the contract repayment frequency), and any remainder in days. For example if you sign a contract today 25th March 2019 and your first payment is 25th April 2019 the time period as a fraction of a year is 1/12 (0.8333). If it were 30th April it would be 1 month + 5 days or 1/12 + 5/365 (0.0970).

This got quite technical very quickly so hopefully it made some sense.

This is a cheeky plug... I recently open-sourced a Typescript/JavaScript financial calculator library which you are all free to use in your own projects.
 
Thanks Andrew (well, I think that I am thanking you!!……..I'll need to get myself a strong coffee before I sit down to get my poor head around this!). I'll definitely take a look at your cheeky plug stuff too. Thanks again.
 
You must log in or register to reply here.
Back
Top