AER vs Gross interest

isasmurf

lipidicman wrote:

Isasmurf. ING indeed have it correct because they compound monthly. So the Gross rate is based on a month and doesn't account for compounding. So it is valid to divide the gross rate by 365 to get a daily rate.

Which is what I said all the back in post 2. All I was saying back then was interest you received based on the closing balance of the account on that particular day, the fact that it is compounded over the months was totally different.

In fairness I think we were talking about the same thing in different ways.

Now, I'm interest in this 365th root business. When I calculate it using this method, I get 1p out. What am I doing wrong? This is using an AER of 4.75% paid and compounded monthly.

               365th root             divisible by 365
             (lipidicman's method) (my method)
Daily Rate   0.00012714		  0.00012739

Jan	31	100.39	  	  100.39
Feb	28	100.75		  100.75
Mar	31	101.15		  101.15
Apr	30	101.53		  101.54
May	31	101.93		  101.94
Jun	30	102.32		  102.33
Jul	31	102.73		  102.73
Aug	31	103.13		  103.14
Sep	30	103.53		  103.53
Oct	31	103.93		  103.94
Nov	30	104.33		  104.34
Dec	31	104.741		  104.750

tomstickland

That's because the 365th root has to be applied and compounded 365 times to arrive at the same annual rate.
How did you compute your rows in that example?


I'd like to go back to absolute basics here.

When a bank quote an annual gross rate of x%, what do they mean? As I've started to realise, there are many ways of calculating and paying interest. But, what, in the first instance, does an annual gross rate mean? It suggests that it is the annual rate (LOL), but if it's calculated daily and paid monthly then that's not an annual rate is it? The AER has a clear definition.

miller

tomstickland wrote:

The AER has a clear definition.

Without wanting to muddy the waters further, the AER is unclear when you take tax into account and frequency of interest compounding.

e.g. you can have 2 accounts paying the same AER, but compounding interest on a monthly and annual basis. I believe the annual one was better as the tax man hasn't had the chance to take his cut.

miller

Another thing I'll add to this is the banks could easily include the formula used to calculate interest on their paperwork. Often they say you can ask for it - probably so they can have a good laugh.

...however, there was a report a while back that some banks weren't paying the correct interest.

isasmurf

tomstickland wrote:

That's because the 365th root has to be applied and compounded 365 times to arrive at the same annual rate.
How did you compute your rows in that example?

Now this is what I thought, but you lot seem to be so insistent on this. Please show me a bank that compounds (savings) interest on a daily basis, because I do not know of one, and I'd be interested in opening an account there. I think there are some loans and mortgages where the 365th root could be valid because interest is calculated and compounded on a daily basis.

I'd like to go back to absolute basics here.

When a bank quote an annual gross rate of x%, what do they mean? As I've started to realise, there are many ways of calculating and paying interest. But, what, in the first instance, does an annual gross rate mean? It suggests that it is the annual rate (LOL), but if it's calculated daily and paid monthly then that's not an annual rate is it? The AER has a clear definition.

Do banks quote "annual gross interest". I thought it was just "gross interest" which as I understand it reading the BBA's code of conduct for advertising interest bearing accounts (savings acounts to you and me) is the contractual rate of interest on which interest on your savings are calculated (oh dear, we're back to the beginning again! :rolleyes: ).

The BBA link grumbler posted above is very useful. I suggest people read paragraph 7.

tomstickland

Well, the thing is, regardless of what it's called, if the bank said "we caclulate your interest using the following set of rules" then I could work out for myself what that essentially means.

Without wanting to muddy the waters further, the AER is unclear when you take tax into account and frequency of interest compounding.

e.g. you can have 2 accounts paying the same AER, but compounding interest on a monthly and annual basis. I believe the annual one was better as the tax man hasn't had the chance to take his cut.

Ah. My understanding of AER was that it tells you how much you gain over a complete year if you just put £x in at the start and leave it there.

With regard to the daily compounding vs annual rate/365 paid daily thing, I don't know which is correct and won't know until I can start from the commonly agreed definitions. For example, if the bank say "our gross rate is y%" then I don't actually know what that means in terms of daily rate".

So, a lot of confusion. But I believe that if we can work through all of the confusion we can end up with a definitive explanation of all of these various things. This can then be written up and put on a web page and referred to every time the same questions come up again in the future.

charlieboycat

isasmurf wrote:

Please show me a bank that compounds (savings) interest on a daily basis, because I do not know of one, and I'd be interested in opening an account there.

Egg calculates interest like this on its savings accounts - see it's FAQs [How is my interest calculated? - Interest is calculated on a daily compound basis.]

Having had one of their a/cs when it was paying 5.5% last year I can confirm that they do indeed calculate it this way (they compounded daily at a daily gross rate of 5.3545%).

Since it saves them money in circumstances where the saver closes the account before the normal interst payment date (which we all do all the time on a/cs offering 6 month bonuses) I don't understand why all banks don't do this.

tomstickland

Aha, a moment of clarity has occured for me.

Forgetting about compounding, they pay 5.5% per year, but they pay it daily. So, without compounding, over a year they would pay you 5.5% of the start sum. So, each day they pay 1/365th of this.
Hence, each day they pay 0.055/365 which is 0.000147 of the amount paid in at the start.
If they compound it daily, then the daily multiplier is 1.000147 and they compound this 365 times. Hence the annual multiplier is 1.000147^365 which is 1.054953.
ie: AER is 5.5%.


So, my understanding of gross annual rate now is that it's the money that they pay as interest, but not including any gains from compounding.

tomstickland

As a further thought,taking that daily multiplier and calculating the interest daily, but paying it monthly would change the sums slightly.
Each day you have 0.000147 of the account balance added to the interest stash. Then at the end of the month this is paid. So for an average month you get 366/12 days of 0.000147. This gives an average monthly multiplier of 1.004458. Compund this 12 times and you get 1.05488, which is 5.488%. It's a nat's todger different from the 5.495% calc above. On £1000 it'd made a 7p difference over the year.

chickpea

I'm too lazy to do the maths, and I can't even keep up with how much I have saved up.

But last month, I had about 32 grand with ING and they paid me 100 quid interest.

I was well pleased!

This month, I have ended up with about 35 grand, so I expect about 110 quid.

Next month I expect to have 38 grand and expect 120-130 quid interest.

Thsi is a great bank!

I never need to speak to a soul - just push button transfers in from my current account, and check my balance now and then.

Easy as pie. Why anyone would put themselves through the agony and risks of ICICI for the sake of an extra 10-20 paltry quid beats me. Plus, ING encourages you to put more and more in, to see the figures - and free money - increase more and more. Fab.