Interest calculated, accrued, paid - what they all mean and which is best

RG2015

spider42 said:

RG2015 said:

spider42 said:

Martico said:

TheLittleThings said:

I've looked at various sources online and still can't get my head around this, so please explain simply if possible! 

Is Bernoulli's inequality simple enough for you?

LOL! Sorry - lost sight of the OP's original request! But AmityNeon's first post in this thread already provides an exceptionally good and concise summary of the main things to consider when choosing between monthly and annual interest (mainly tax), and when differences between the two will arise.

Too many people incorrectly believe that a monthly account with the same AER as an annual account will always pay the same amount of interest as the annual account. In general, that will only be the case if the balance is left untouched for the full year and the interest rate doesn't change. But the differences will generally be fairly
small.

Another opportunity with annual accounts is 'self-compounding'. In other words, if you close the account, all of the accrued interest is added on closure, so you get the interest paid earlier than usual. You can then reopen a similar account, and earn interest on the interest, so you get the higher annual interest rate, plus the benefits of compounding too.

E.g. if you leave £100k earning 5% for a year, you get interest of £5,000, so closing balance is £105,000. If you instead close the account after 6 months, you get £2,500 interest, so have a closing balance of £102,500. Put that in another account paying 5% for the next 6 months, and you've got £102,500 plus 2.5% = £105,062.50 at the end of the year. So the closure has generated an additional £62.50 of interest.

5% monthly equates to 5.12% AER.

£100,000 @ 5.12% = £105,120.

To my knowledge banks don’t pay the same rate for monthly as annual interest. Hence your £62.50 gain is fundamentally flawed

That example is comparing an account paying 5% annually and held for a full year to an account paying 5% annually which is closed after 6 months and then put into a new annually paying account. No monthly interest is involved, so I'm not sure how you come to the conclusion it is "fundamentally flawed".

I started it off with "Another opportunity with annual accounts is .... " so I'm not sure why you think I'm talking about monthly paying accounts here?

Okay, I understand, but I have a question.

If you have an account with £100,000 that is paying 5.00% AER, will you get £2,500 in interest if you close it after 6 months?

I had not considered this, and it just seems odd to me, particularly given the possibility to earn an extra £62.50 in your scenario.

spider42

slinger2 said:

If you're getting 5% gross/year paid monthly, your getting 5%/12=0.417% per month. After one month you'd have £100,417, after two months you'd have 100000*(1.00417)^2=£100,835 and after 12 months you'd have 100000*(1.00417)^12=£105,120. That's how 5% gross becomes 5.12% AER.

I am a Chartered Accountant, and have a first class degree in maths. I'd like to think that I understand how to calculate an AER!

For the avoidance of doubt, in my most recent example, THERE ARE NO MONTHLY PAYING ACCOUNTS. Therefore AER is irrelevant. The example assumes the account pays 5% ANNUALLY.

If you put in £100,000 at 5% and leave it for a year, you end up with £105,000 after 12 months.

If you instead close the account after 6 months, you get interest of £2,500, so you then have balance of £102,500. Put that £102,500 in another 5% account (annual), and then close after 6 months. You get 5% interest on £102,500, for 6 months, which is £2,562.50. You end up with £105,062.50. The closing manoeuvre has increased the interest by £62.50.

spider42

RG2015 said:

spider42 said:

RG2015 said:

spider42 said:

Martico said:

TheLittleThings said:

I've looked at various sources online and still can't get my head around this, so please explain simply if possible! 

Is Bernoulli's inequality simple enough for you?

LOL! Sorry - lost sight of the OP's original request! But AmityNeon's first post in this thread already provides an exceptionally good and concise summary of the main things to consider when choosing between monthly and annual interest (mainly tax), and when differences between the two will arise.

Too many people incorrectly believe that a monthly account with the same AER as an annual account will always pay the same amount of interest as the annual account. In general, that will only be the case if the balance is left untouched for the full year and the interest rate doesn't change. But the differences will generally be fairly
small.

Another opportunity with annual accounts is 'self-compounding'. In other words, if you close the account, all of the accrued interest is added on closure, so you get the interest paid earlier than usual. You can then reopen a similar account, and earn interest on the interest, so you get the higher annual interest rate, plus the benefits of compounding too.

E.g. if you leave £100k earning 5% for a year, you get interest of £5,000, so closing balance is £105,000. If you instead close the account after 6 months, you get £2,500 interest, so have a closing balance of £102,500. Put that in another account paying 5% for the next 6 months, and you've got £102,500 plus 2.5% = £105,062.50 at the end of the year. So the closure has generated an additional £62.50 of interest.

5% monthly equates to 5.12% AER.

£100,000 @ 5.12% = £105,120.

To my knowledge banks don’t pay the same rate for monthly as annual interest. Hence your £62.50 gain is fundamentally flawed

That example is comparing an account paying 5% annually and held for a full year to an account paying 5% annually which is closed after 6 months and then put into a new annually paying account. No monthly interest is involved, so I'm not sure how you come to the conclusion it is "fundamentally flawed".

I started it off with "Another opportunity with annual accounts is .... " so I'm not sure why you think I'm talking about monthly paying accounts here?

If you have an account with £100,000 that is paying 5.00% AER, will you get £2,500 in interest if you close it after 6 months?

Yes, with an annual paying account, you would. 5% is the contractual interest rate. The interest accruing is 5%/365 (or possibly 5%/366 in a leap year) for each day each pound is in there. In half a year, you've accrued half the interest (or more accurately you get the full interest rate, but for half the length of time).

(At the risk of causing more confusion, with a monthly paying account with 5% AER, you would have £102,469.51 after 6 months).

RG2015

@spider42

Thank you for your reply. I have learned something new today.

I had always thought that an account paying 5.00%pa AER that was closed after 6 months would earn less than 5.00%pa.

I thought that AER was to factor in compounding and could only be achieved after 12 months.

It is even more suprising that the banks would allow themsevles to lose out financially to a clever arithmetic scheme.

It just goes to show the dangers of assuming things without any evidence. 

RG2015

spider42 said:

slinger2 said:

If you're getting 5% gross/year paid monthly, your getting 5%/12=0.417% per month. After one month you'd have £100,417, after two months you'd have 100000*(1.00417)^2=£100,835 and after 12 months you'd have 100000*(1.00417)^12=£105,120. That's how 5% gross becomes 5.12% AER.

I am a Chartered Accountant, and have a first class degree in maths. I'd like to think that I understand how to calculate an AER!

For the avoidance of doubt, in my most recent example, THERE ARE NO MONTHLY PAYING ACCOUNTS. Therefore AER is irrelevant. The example assumes the account pays 5% ANNUALLY.

If you put in £100,000 at 5% and leave it for a year, you end up with £105,000 after 12 months.

If you instead close the account after 6 months, you get interest of £2,500, so you then have balance of £102,500. Put that £102,500 in another 5% account (annual), and then close after 6 months. You get 5% interest on £102,500, for 6 months, which is £2,562.50. You end up with £105,062.50. The closing manoeuvre has increased the interest by £62.50.

I am still struggling to get my head around this extra £62.50.

The interest rate is 5.00% AER. If paid annually, the interest earned is £5,000. 

However in your example, the interest earned is £5,062.50.

£5,062.50 / £100,000 = 5.0625%

Is the interest rate 5.00% AER or 5.0625% AER?

spider42

The AER calculation works out the equivalent annual interest rate of you depositing a sum of money, and leaving it untouched for 12 months. Hence the name "Annual Equivalent Rate". On a monthly paying account the actual interest rate will be lower (about 4.89% on a 5% AER account). But because of compounding if you had a 4.89% account paying monthly, you would end up with £105,000 over the year. So the AER is 5%. They are "equivalent" over a year, which is different from them being equal in all eventualities. 

What confuses pretty much everyone (AmityNeon is about the only person I've seen on here who appears to understand it) is that the formula which calculates AER will generally only result in the same total interest at the end of the 12 months if all of the assumptions made in deriving the gross interest rate on a monthly account hold true. In other words, if the balance remains constant over the year, and if the interest rate remains constant over the year. If either the balance changes, or the interest rate changes, then monthly and annual interest will usually give different results (although, as mentioned before, they will usually be pretty close).

So to answer your question the interest rate on the account in question would be 5%, and the AER of that account would also be 5%. The AER calculation works on the basis that the money is left untouched for a year. But here, it isn't being left untouched, therefore the interest is different than what the AER figure would suggest.

By closing and reopening after 6 months, you've effectively turned it from an account paying 5% interest annually, to one paying 5% interest bi-annually. If a bank offered an account paying a gross rate of 5% every 6 months, then the AER of the account would indeed be 5.0625%. But you've effectively artificially created that scenario. The account you actually own still only pays annually, so the AER quoted on that account will be 5%. But the interest you have received is equivalent to a rate of 5.0625%.

zagfles

AER is also supposed to account for cashflow where that's known. I remember being confused by a regular saver account which paid interest annually at 6% nominal but the AER was something like 6.1%. Reason was the mandated cashflow on the account meant the balance was higher when nearer to the interest payment date. AER is more complicated than simply accounting for compounding. 

RG2015

@spider42

Once again, many thanks.

Can I ask your opinion on why the banks would allow a strategy that in effect lost them £62.50?

I had assumed that they would migigate against such an outcome by applying a monthly/gross interest rate equivalent for an account closure before the annual interest payment date.

zagfles

RG2015 said:

@spider42

Thank you for your reply. I have learned something new today.

I had always thought that an account paying 5.00%pa AER that was closed after 6 months would earn less than 5.00%pa.

I thought that AER was to factor in compounding and could only be achieved after 12 months.

It is even more suprising that the banks would allow themsevles to lose out financially to a clever arithmetic scheme.

It just goes to show the dangers of assuming things without any evidence. 

It's trivia to them and too much hassle for too little gain for anyone to bother taking advantage of it. Another way would be to open several accounts at 5% paid annually but with different interest payment dates, and shift money into the account which pays interest soonest, then once paid shift to the next interest payer. Then you can compound the interest. But again, gain will be trivial. 

RG2015

I have also been confused by the interest rates being quoted as AER/Gross.

For example, AER 6.17% / Gross 6.00% for the NatWest digital regular saver. Gross to me has always meant before tax as opposed to net after tax.

The term gross makes no sense when all it means is not AER. It makes more sense to consider that this is the equivalent rate if interest was paid monthly. Hence my use of the term monthly in an earlier post.

An example of this is the Ford Money Flexible saver which quotes 4.60% AER / 4.51% monthly.