A&L - Interest Payment Date Question

YorkshireBoy

Jumping_Bean wrote: »

But I thought the whole point of daily compound interest was that it was "capitalised" daily.

Interest accrued does not capitalise (or compound) until it is paid. I've never seen a savings account paying "daily compound interest"...have you?

Any 2 ISA accounts with the same AER pay the same amount of interest in a given time.

Not according to my worked example above they don't.

jamesd

YorkshireBoy, it's hard to work out just where and why you're getting it wrong mentally but I'll try some approaches that might work.

Dividing by 365 to get daily interest is an approximation to compound interest that always produces higher results than reality for shorter periods. That means that it's giving your calculation higher interest than is really due for both portions of the A&L calculation.

When you wrote that interest is calculated daily, that's the correct calculation. You're not calculating daily but calculating annually and dividing by the number of days in the year. That gives the first days a portion of the interest on the interest from the later days. That last sentence may be the key to understanding why there's a problem with your calculations.

The approximation is fine for rough work and because it pays too much for short periods it's fine as a way for a bank to calculate how much to pay a customer when correcting an interest underpayment mistake - the error favors the consumer.

If you use the real compound interest calculations, here's how it works for A&L:

3,600 x 1.0625 ^ (270/365) = 3,765.12

(In Windows calculator ^ is the x^y key that you see if you use scientific mode)

3,765.12 x 1.0625 ^ (95/365) = 3,825

And for the single annual calculation it's:

3,600 x 1.0625 = 3825

This is consistent with A&Ls declaration that you "Earn 6.25% gross p.a./AER", since it produces the correct result that gross and AER are the same.

If A&L wanted to pay more interest than they say they pay they could calculate it as you describe. No reason for them to choose to do that, though.

Jumping_Bean

YorkshireBoy wrote: »

Interest accrued does not capitalise (or compound) until it is paid. I've never seen a savings account paying "daily compound interest"...have you?Not according to my worked example above they don't.

So let me get this straight... You're saying that (With all other factors being equal) an ISA that pays interest monthly pays out more than one that pays interest annually?

If so, I think you're the first person I've come across that believes that. Every other view I've read on this site and other sites have said that if the AERs are the same then it makes no difference when the balance of the accounts are updated - The accounts will perform the same.

Can you point me to another post by another user that shares your view? I may well be wrong but i would just like to confirm one way or the other.

YorkshireBoy

Jumping_Bean wrote: »

So let me get this straight... You're saying that (With all other factors being equal) an ISA that pays interest monthly pays out more than one that pays interest annually?

No, I'm not. You're the one who keeps mentioning monthly interest.

I'm specifically talking about the A&L account (which pays interest once per year on 1st Jan), and the amount of interest that would be paid in total over a tax year if the account was opened on 6th April and closed on 5th April the following year.

Jumping_Bean

YorkshireBoy wrote: »

No, I'm not. You're the one who keeps mentioning monthly interest.

I only keep mentioning monthly interest because you said this:

YorkshireBoy wrote: »

Interest accrued does not capitalise (or compound) until it is paid.

By that logic the more often an account capitalises / compounds / pays interest the more it should pay. Therefore an account that does this monthly should pay more than one that does it annually. No?

YorkshireBoy wrote: »

Not according to my worked example above they don't.

In light of what jamesd said above do you still stand by this or do you now acknowledge that your example is incorrect?

YorkshireBoy

Jumping_Bean wrote: »

By that logic the more often an account capitalises / compounds / pays interest the more it should pay. Therefore an account that does this monthly should pay more than one that does it annually. No?

No, because (so long as there isn't an introductory bonus applicable) monthly paying interest accounts have a lower gross p.a. figure than their quoted AER figure. Only after monthly compounding (x 12) of the gross p.a. figure do you achieve the quoted AER figure.

In light of what jamesd said above do you still stand by this...

I don't think we'll know either way, because we don't know how A&L calculate the interest. For example, do they use James' method, or the method quoted by other providers such as ING who say...

Interest on your savings account is accrued daily...

Daily closing balance (cleared balance) x interest rate (as a percentage) / Number of days in calendar year = one day's worth of interest

Indeed, James said "If A&L wanted to pay more interest than they say they pay they could calculate it as you describe. No reason for them to choose to do that, though."

or do you now acknowledge that your example is incorrect?

Why are you challenging me? I stated it was my "understanding"...not that it was fact.

YorkshireBoy

jamesd wrote: »

...snip...

The thanks button doesn't work for me on this PC James, so thank you for your post.

I suppose unless, and until, we know how A&L calculate interest, we can't conclude the discussion.

Just to reiterate, I'm only posting my understanding...not saying how it is.

YorkshireBoy

It appears it's far from straight-forward.

From the BBA website...

The AER is a notional rate – it is not necessarily equal to the cash return because, in calculating it, we make assumptions:

http://www.bba.org.uk/bba/jsp/polopoly.jsp?d=135&a=1575&artpage=1

...the key word being "assumptions".

Maybe A&L and ING, for example, make different assumptions?

Jumping_Bean

YorkshireBoy wrote: »

No, because (so long as there isn't an introductory bonus applicable) monthly paying interest accounts have a lower gross p.a. figure than their quoted AER figure. Only after monthly compounding (x 12) of the gross p.a. figure do you achieve the quoted AER figure.

Which is exactly my point. 2 ISAs with the same AER pay the same amount of interest regardless of the date and frequency the balance of the accounts are updated.

YorkshireBoy wrote: »

Why are you challenging me? I stated it was my "understanding"...not that it was fact.

I was challenging you because I didn't necessarily agree with what you said. I don't think there's anything wrong with that. Would you not do the same?

If you were correct I wanted to know. If you weren't it's probably better if it's out in the open in case the OP or someone else chooses an account based on the info you provided. I wasn't trying to offend you, I was just trying to see if with hindsight, you agree with what James said or if you stood by your initial figures. You've now answered this so it seems to have achieved its purpose.