Re: AER - Halifax don't know either

Here's my reply requesting further clarification:

--quote Thank you for your comprehensive reply of 2nd April to my query of

20th March.

Unfortunately it appears that you have misunderstood the nature of my concern. I am not interested in the fact that the AER has greater prominence in your material than has the gross rate. My problem is that it has a greater numeric value.

The nature of my query is one of technical compliance. If you have a compliance department, perhaps you could seek advice from them. There must be someone in the team responsible for the content of your material, who understands the technical issues and can comment.

Essentially your material alleges three facts:

1) That the contractual rate is 6.00%. 2) That the AER is 6.05%. 3) That interest is paid only once at the end of the year.

What I am saying is that it is impossible for more than two of these facts to be true, and I'm trying to discover which one is false.

I draw your attention to the BBA's Code of Conduct for the Advertising of Interest-Bearing Accounts, which in its AER appendix, available at

confirms that:

"If an account pays or credits interest once a year, then the AER is equal to the gross rate."

Therefore, since your AER is greater than the gross rate, it follows that interest is paid more frequently than yearly. I look forward to receiving a more technical reply which explains why your experts think the AER in the specific circumstances of this account is not equal to the contractual gross rate.

--unquote

Notwithstanding the further letter I wrote to Halifax today, I think I've nevertheless cracked it. I look forward to learning whether Halifax's reply, when it comes, confirms my conclusion.

My thinking now goes along the following lines:

If an account pays interest only once, at the end of one year, at a nominal rate of 6%pa or 0.5%pm, and the conditions are that you place a fixed sum on deposit at the start of the year and it stays there all year and you make no withdrawals or further deposits, then clearly the AER and gross rate will both equal exactly 6%.

If an account pays interest only once, at the end of *one month*, at a nominal rate of 0.5%pm, and the conditions are similar to above, that the deposit remain there undiminished and unaugmented for the duration of the period (in this case one month), then we really have an interest application *frequency* which is monthly, even though the interest application only actually happens once. The AER then must be 6.1678%.

If you view the actual Halifax Regular Saver account, for which the conditions are that you deposit the same amount regularly each month, as 12 separate accounts, one lasting for 12 months, one for

11, one for 10, etc, and one for 1, then the AERs of each will take various values between 6.00 and 6.17%, reflecting the fact that the "frequency of compounding" for each will vary beteen "every N months" where N takes all values between 1 and 12, and so the effective composite AER must lie between those values. Obviously it won't be the simple arithmetic mean, but a first crude approximation by weighting the 6.0000 by 12, the 6.1678 by 1, and the inbetween ones by factors 2 to 11, gives me the result 6.0550%, which is a close call between an official 6.05% result and 6.06%. In fact, working to more decimal places, the crude weighting gives an answer which would officially have to be 6.06%, namely 6.05500472%.

When I get a moment I'll apply the full gory formula given in

the one with those nasty-looking big sigmas and big pi, but rebased to monthly instead of annual periods, and then reverted to annual. It may well give an answer a hair's breadth under 6.055% which would justify the quoted 6.05%.

AER's are always rounded down to 2 d.p. (like APR's used to be rounded down to 1 d.p. many moons ago)

In message , Ronald Raygun writes

I think you've cracked it there RT, BUT it just goes to show how AER (like APR) can actually mislead us.

Ive had a quick look again through the aer link you posted but the overriding rule seems to be this 'once a year' thing, which (unlike APR) doesn't take account of mid-year application of interest.

I await the next instalment......................

Done properly: Assume you invest £100pm. Using contractual 6% this means at the end of the year you will have capital of £1200 plus interest of £100 x 0.005 x (12+11+..+1 = 78). Total = £1239 (in theory exactly, assuming payments are made at intervals of exactly one month; in practice there is no such thing as an exact month, as deposits are made on a granularity of days, and interest is calculated on a daily basis too, so the answer is approximate).

The AER will be that rate which makes the sum (i = 1 to 12) of £100 x f^(i/12) equal to £1239, where f = 1+AER/100. Indepenent of amount invested, we must have the sum (i = 1 to 12) f^(i/12) equal to 12.39. Turns out f is 1.060543683154336 or so, and hence the rounding *down* from 6.054...% to 6.05% is justified.

Not true. The BBA worked examples show cases where they round up and where they round down. So they evidently round to nearest.

I stand corrected!