From: "Tim" 
Newsgroups: uk.finance
Subject: Re: Compound intereset calculators - different results.
Date: Fri, 8 Apr 2005 19:44:15 +0000 (UTC)

> "Tim" wrote
> >As an aside, do you know of any banks which
> >actually compound interest "annually" after *3* months,
>
"john boyle" wrote
> Im not sure what you mean, do you mean the first interest is
> credited to the account after 3 months then annually thereafter?

Yes, that is what I mean.
The nominal rate you quoted would only be correct for an account opened on 1
Jan with AER=10% and withdrawal on 31 Dec - meaning the interest is credited
after 3 months.  We know A/c2 has interest paid annually, because that was
part of its definition - so it would be annually thereafter (after the first
3 months after opening).

> "Tim" wrote
> >And if so, is it really *legal* to quote AER=10%
> >when nominal rate is only 9.819% ??
>
"john boyle" wrote
> Yes. AER and its use is not defined in law.
> Its just an agreement between banks.

In that case, I'm glad I never trust any AER quotes!

> "Tim" wrote
> >Because in that case, if someone invested £10,000 for exactly
> >ten-and-a-quarter years (ie up to an interest application date),
> >they'd only get £26,140 at the end.  That's an equivalent annual
> >rate of only 9.83% (ie much lower than the 10% quoted) ....
>
"john boyle" wrote
> If you mean that the interest is compounds annually and the £10k
> is credited in month 9 of the first year then I get £26585.86.

The interest is credited at the end of the third month (31 March after
opening 1 January) :-

Just after the first interest, they'd have £10K x (1 + 0.25 x 9.819%) =
£10,245.
Then after 1.25 years (from the start), they'd have:  £10,245 x 1.09819 =
£11,251.
Then after a further 9 years, they'd have:  £11,251 x 1.09819^9 = £26,140.