AER vs Gross interest

gibbo888

Hi All

I am getting a bit confused with all this aer/gross malarky on the savings accounts which are going around. Can someone plesse clarify a few things for me.

Cahoot pay 5.25% Gross and 4.93% AER.
Forget bonuses and mininum amount invested bla bla bla.
just straight forward math.
\if i put £100 in this account for exactly a year would it be worth £105.25 OR £104.93? (non tax payer)

BUT

ING pays 4.65% Gross and 4.75% AER.
so assuming the same above

equates to £104.65 Gross OR £104.75 AER???

I am totally confused, different aer figures against gross figures.

Could someone explain in "simple" easy to understand terms how aer works and what it means PLEASE!

Mike

isasmurf

I'll get in before Grumbler comes on with his complicated mathematics...

In as simple terms as I can put it, the interest you get paid is based on the gross amount. So if the gross is 5% the interest will be calculated at 5%/365 per day. The AER is the interest you would receive over the course of the year on your original deposit, if you deposited no more money, had the interest paid into the account and didn't withdraw any money from the account including the interest.

You will find that accounts that pay interest monthly have different gross/AER rates. This is because the interest (calcualted at the Gross rate) you receive on your original deposit is calculate daily and paid at the end of the first month. This interest then starts accumulating its own interest for the next month and that gets paid and starts earning its own interest and so on... This is known as compounding.

Accounts with bonus rates will have different Gross/AERs because for part of the year you are earning interest at the higher gross rate, and then when the bonus expires you start earning interest at the lower gross rate. The AER will state what interest you have received over the course of the year based on the conditions stated above.

You will find that accounts that pay interest annually (and have no bonus rate) will have the same gross/AER. This is because there is no compounding (interest receiving its own interest) and the same interest rate applies throughout the year.

So in your examples above, you would have £104.93 in Cahoot, and £104.75 in ING Direct.

Robert_Sterling_3

The Cahoot rate is actually 5.25% gross for six months.
After that it is 4.50% for six months.
If you put £100 in and leave it in then after 6 months you get interest at the rate of 5.25% per annum for half a year
i.e. You get £2.625 interest
In the second 6 month you get interest at the rate of 4.5% per annum on £102.625 for half a year.
The interest is £2.309.

So the total interest is £2.625 plus £2.309 = £4.934

We ignore the .004 of 1p leaving £4.93

Thus on £100 for 1 year you get the same amount as if you were paid 4.93% for 1 year.

That is why it is called the annual Equivalent Rate or AER

5.25% for 6 months then 4.5% for sixth months with interest paid each six months is equivalent to 4.93% per annum paid at the end of 1 year.

Astute Investors may get 5.25% per annum for six months and then close the account.


The use of the word gross in this context means before tax has been deducted.

5.25% Gross is 4.2% Net of tax at 20p in the £ and is 3.15% net of tax at 40p in the £.

YorkshireBoy

gibbo888 wrote:

Could someone explain in "simple" easy to understand terms how aer works and what it means PLEASE!

Providers must quote AER's on all savings products. AER's are the only way accurately compare products with monthly/annual interest and to factor in the effects of introductory bonuses. Using the examples given...

£100 in ING for 12 months, with interest paid monthly...

Month......Balance.....Int Rate.....Interest
1.............100.00......4.65%.......0.39
2.............100.39......4.65%.......0.39
3.............100.78......4.65%.......0.39
4.............101.17......4.65%.......0.39
5.............101.56......4.65%.......0.39
6.............101.95......4.65%.......0.40
7.............102.35......4.65%.......0.40
8.............102.74......4.65%.......0.40
9.............103.14......4.65%.......0.40
10...........103.54......4.65%.......0.40
11...........103.94......4.65%.......0.40
12...........104.35......4.65%.......0.40
13...........104.75

The monthly gross rate is 4.65%. The interest is added and compounded monthly, giving an AER (annual equivalent rate) of 4.75%.


£100 in Cahoot for 12 months, with interest paid monthly...

Month......Balance.....Int Rate.....Interest
1............100.00......5.14%.......0.43
2............100.43......5.14%.......0.43
3............100.86......5.14%.......0.43
4............101.29......5.14%.......0.43
5............101.72......5.14%.......0.44
6............102.16......5.14%.......0.44
7............102.60......4.65%.......0.40
8............102.99......4.65%.......0.40
9............103.39......4.65%.......0.40
10..........103.79......4.41%.......0.38
11..........104.18......4.41%.......0.38
12..........104.56......4.41%.......0.38
13..........104.93

The monthly gross rate is 5.14% for months 1-6, 4.65% for months 7-9, and 4.41% for months 10-12. The interest is added and compounded monthly, giving an AER (annual equivalent rate) of 4.93%.


£100 in Cahoot for 12 months, with interest paid yearly...

Month......Balance.....Int Rate.....Interest
1............100.00......5.25%.......0.44
2............100.00......5.25%.......0.44
3............100.00......5.25%.......0.44
4............100.00......5.25%.......0.44
5............100.00......5.25%.......0.44
6............100.00......5.25%.......0.44
7............100.00......4.75%.......0.40
8............100.00......4.75%.......0.40
9............100.00......4.75%.......0.40
10..........100.00......4.50%.......0.38
11..........100.00......4.50%.......0.38
12..........100.00......4.50%.......0.38
13..........100.00.........+..........4.93.....=......104.93

Interest is earned monthly but paid annually. Note that the AER is the same for both Cahoot options.

grumbler

isasmurf wrote:

...before Grumbler comes on with his complicated mathematics...

Although I can rest now, I'll add some mathematics :
For ING: 4.65% gross p.a. => 4.65%/12=0.3875% p.m.
(1+0.003875)^12=1.0475 => 4.75% AER

As above: what you actually get is AER. Gross interest does not take compounding into consideration and is convenient to calculate monthly interest just by dividing by 12 (you cannot do this with AER).

lipidicman

I'm with grumbler as usual. However i have a small problem with Isasmurf's post:

'if the gross is 5% the interest will be calculated at 5%/365 per day.'

The gross amount is dependant on the interest frequency. Ie if it is 4.65% gross paid monthly then you can divide by 12, but not by 365. This relates to why an account with monthly and annual options have two different gross rates, but equal AERs (as per grumblers method above).

If the gross rate is 5% paid annually (ie gross rate = AER) then the daily rate will be
1.05^1/365 = 1.0001336806171134403505084797728
or 0.01337%
whereas
5/365 = 0.01370% (which is wrong)
(if it was 'paid monthly' then use grumblers method to work out the AER then proceed as above)

Robert_Sterling_3

I am still of the opinion that the use of the word gross is to indicate that it is the amount of interest before tax.

tomstickland

Useful post this. So it's quite simple really. Gross rate is the rate applied before tax. It's often applied monthly, so by the end of the year you've earnt a bit extra because of the interest on the interest (ie: ompound interest). AER is the yearly gain as a percentage. Whatever happened to APR<q mark>

MarkyMarkD

APR stands for "annual percentage rate of charge" and applies to loans/credit cards.

AER standards for "annual equivalent rate of interest" and applies to savings.

isasmurf

lipidicman wrote:

I'm with grumbler as usual. However i have a small problem with Isasmurf's post:

'if the gross is 5% the interest will be calculated at 5%/365 per day.'

The gross amount is dependant on the interest frequency. Ie if it is 4.65% gross paid monthly then you can divide by 12, but not by 365. This relates to why an account with monthly and annual options have two different gross rates, but equal AERs (as per grumblers method above).

If the gross rate is 5% paid annually (ie gross rate = AER) then the daily rate will be
1.05^1/365 = 1.0001336806171134403505084797728
or 0.01337%
whereas
5/365 = 0.01370% (which is wrong)
(if it was 'paid monthly' then use grumblers method to work out the AER then proceed as above)

Sorry, I disagree. It's easier for most people to work it out that way, but that ignores the fact that interest is calculated on a daily basis for almost all accounts, regardless of whether it is paid monthly or annually.

I've been looking for somewhere to back up my calculation, and struggled for a while, but hey presto... that bank that likes to think it talks to its customers straight (ING Direct) seems to be the only place that tells you how it calculates its interest, which is the same way I calculated above.
http://www.ingdirect.co.uk/html/aboutsavings/faqs.html#interestcalc

tomstickland

Yes, well, a mathematical approximation that is comonly used is:

(1+a)^b = 1 + ab

so if a is the annual percentage expressed as a decimal (eg: 5% is 0.05) and b is 1/12 (to convert from annual to monthly) then the effective rate is APPROXIMATELY 1/12th of the annual rate.

Really you want to take the 12th root (y=x^(1/12)) to convert from annual to monthly and the 365th root to convert from annual to daily (y=x^(1/365)).

As an example, for a 5% annual rate,
true daily rate = (1 + 0.05)^(1/365)=1.000134
simple daily rate = 1 + 0.05/365 = 1.000137
that's a 3% descrepancy of the daily rate, or a much much smaller descrepancy of the daily multiplier.

The simplified daily rate can be converted back to annual rate:
1.000137^365=1.051, so that's 5.1% annual.