ING - Interest Payments

In message , GPG writes

No.

Hmm, can you confirm that no cheques were paid into the account towards the end of November, that you have the interest added to your account monthly and no other transactions took place from 1/12/03 - 31/1/04 other than the credit of interest on 31 Dec. Also, can you confirm that you received the January interest payment on 31 Jan (which was a Saturday)

Why not ask them?

Assuming you hadn't taken ANY money out (including the interest), then my guess is that you should have got more interest on the basis that you wouild get interest on the interest earned in December. I'd query it with them and see what they say.

I'm now going to check my account......

Well, you know, this problem may be tough enough to flummox Boyle, but not me, no Sir. It's really all down to elementary arithmetic, and, of course, a remarkable wee coincidence.

OK, so your balance at the start of December was £10000 (say).

Then December interest should have been £10000*0.0422*0.8*31/365, which is £28.67.

January's interest should be £10028.67*0.0422*0.8*31/366, which, surprise, surprise, is also £28.67.

They do say in their FAQ that the formula for calculating one day's interest involves dividing the daily closing balance times the annual interest rate by "the number of days in a calendar year".

In message , Ronald Raygun writes

Good spot sir!

(Damn....................

Some people !!! I bet he hasn't got many friends :-) He must be quite old to remember leap years - we haven't had one for some time.

All we need now is for him to demonstrate, algebraically, what rate of interest will make the two sums *exactly* equal.

Easy.

Let the balance be 1 (instead of £10k) and the net interest rate be N.

Then December interest will be N*31/365, and January interest will be (1+N*31/365)*N*31/366. For the two to be equal, 31*N cancels out and we're left with 366 = 365+31*N or N = 1/31.

That makes the gross rate 1/24.8 or 4.0323%.

Surprising that it still works to within less than a penny even for a ten grand balance, when the rate is 4.22%, which isn't really all that close to 4.03%.

"GPG" wrote

What, like the usual *four* years ago? [Year 2000] :-)

That, of course, is the answer I got too :-)

However, I was struck by the "0.8" bit. For, taking the tax off monthly results in there being less capital to roll up each month. It having been established that I am indeed paranoid, I could not help suspecting that the AER might turn out to be less than the advertised 4.3%, as a result. And indeed - it is!

For, let C = Capital, and simplifying each month to 1/12 of a year, we receive C * (1 + 0.8*.0422 / 12) ^ 12 = C * 1.0343 or interest of .0343 * C which gives an AER of 3.43 * 1.25 = 4.286 %.

If the tax were removed at the end of the year, we get C * (1 + 0422 / 12) ^ 12 = C * 1.043 which gives an AER of 4.3 % and we receive 0.8 * 4.3 % = 3.44 % nett or interest of .0344 * C

If C = £10,000, we are swindled out of .0001 * £10000 = £1 or so.

So - who is paranoid now? :-))