Calculating daily interest

Pagan98

I'm trying to check the interest paid on my wife's ICICI HiSave account. The interest is calculated daily and paid monthly, except in the first month when the interest due is carried over to the second month (and therefore not compounded). The account is not subject to tax.

My calculation:
AER 5.40% = 12*((1+0.054)^(1/12)-1) = 5.27% gross p.a.
Daily gross interest = 5.27%/365 = 0.014%

01.08.05 to 22.08.05 (22 days) balance of £1.00, interest earned £0.003
23.08.05 to 01.09.05 (10 days) balance of £101.00, interest earned £0.146
02.09.05 to 19.09.05 (18 days) balance of £871.00, interest earned £2.264
20.09.05 to 30.09.05 (11 days) balance of £1,286.00, interest earned £2.043
Total interest earned 01.08.05 to 30.09.05 = £4.45

This assumes savings earn interest from and including the date of deposit. Even if savings earn no interest on the actual day of deposit, I still calculate the interest earned to be £4.27.

ICICI calculate the interest earned as £3.79, quite a difference. The calculation should be relatively straight forward but I get a difference answer to ICICI so who is wrong and if its me, why?

TIA.

DocProc

I think you are probably calculating interest on uncleared funds.

Try the calculation again, but this time, whenever you make a credit entry into the account, allow it 3 days to clear.

I'm not sure whether 3 days is the correct amount of time to use for the calculation but you can also try it again using 2 days for clearance instead.

charlieboycat

Humm ... Assuming deposits were made by direct debit then ordinarily there wouldn't be an "uncleared funds" shortfall - in my experience this is never an issue with other deposit-takers when deposits are made by direct debit (which is why I usually prefer direct debit to BACS - the latter costs 2 days interest). However various comments have been posted about ICICI's direct debiting methodology and the fact that in some cases they credit your HiSave account well in advance of debiting your linked bank account. What happens if you redo your calculations using the dates the funds left your linked account rather than dates they were credited by ICICI?

Pagan98

Thanks for the replies. I tried rejigging the calculation to take account of 2 or 3 days for deposits to clear and also using the date funds left my linked account. None of these gave the answer according to ICICI.

My understanding of the clearing process is that a temporary hold is placed on the funds to ensure that they are received from the other account. I thought that the effective date for interest purposes was when the deposit is posted to the account, rather than when the funds clear.

I tried a similar calculation on my ING Direct account and obtained the same result as ING, so it appears to be some peculiar artifact of the way ICICI calculate interest. I've posted a query to the "account manager" and will share the response when received.

DocProc

We mustn't get too confused about the fact that funds can be claimed back from the linked current account bank.

A Direct Debit would normally take three days to clear. Interest cannot yet be paid until they are cleared.

A CHAPS payment, for example, uses cleared funds. There is no need to wait for funds to clear with this method of banking transfer. Thus the savings account can start to pay interest immediately.

charlieboycat

DocProc wrote:

A Direct Debit would normally take three days to clear. Interest cannot yet be paid until they are cleared.

Perhaps I am misunderstanding what DocProc is saying (I have no idea why direct debit funds might ever be regarded as "uncleared", or whether they can ever be recalled once they have left the sourcing account) but in my experience (with the exception of ICICI):

Funds appear as a receipt/credit to the receiving account on the same date as they are debited to the sourcing account.

In the receiving account they earn interest either from the date they are credited (Birmingham Midshires, Cahoot, Capital One, Egg, ING, Intelligent Finance - ie. those whose T&C say interest accrues from date of receipt) or from the following day (Alliance & Leicester, Bradford & Bingley - ie. those whose T&C say interest accrues from the day after receipt).

This is why, when there is a choice, I prefer to move money by direct debit rather than by BACS. Initiate a BACS transfer on Working Day 1 and it invariably arrives on Working Day 3 (except from Cahoot, from whom it arrives on Day 4) - resulting in a minimum of two days lost interest. However, initiate the same transfer by direct debit instead on Day 1 and it doesn't leave the sourcing account until the day it arrives (usually Day 3, but Day 5 to Cahoot) - thus avoiding the 2 days lost interest.

Of course initiating a CHAPS transfer on Day 1 gets it there on Day 1 - and thus saves two days of lost interest when compared to BACS (still probably only worth it for transfers of £100k+). But it only saves two days of the interest differential compared to a direct debit - and is therefore unlikely to be cost effective unless moving £100k+ from a sourcing account that is of the 0.1% variety.

isasmurf

I think they may have deducted tax. Although it still doesn't quite match taking 20% off your figure, is a lot closer to their figure. The best thing to do is to ask them.

Robert_Sterling_3

Pagan98 wrote:

Daily gross interest = 5.27%/365 = 0.014% TIA.

I do not like this bit.

You managed to get an approximately correct answer for the Monthly Rate from the AER by taking a 12th root.

This may be making assumptions that all months are of equal lengths.

However you seem to have produced a daily rate from a yearly rate by dividing by 365 where perhaps you should have taken the 365th root.

Pagan98

You managed to get an approximately correct answer for the Monthly Rate from the AER by taking a 12th root.

No, I think this is correct. The significant criteria is how often interest is paid/compounded.

The Banking Code guidelines state that the AER is calculated from the gross annual rate by this equation:

AER = 100 * ((1 + gross rate pa /(payment frequency *100))^payment frequency - 1)

The reverse expression is:

gross rate pa = 100 * payment frequency * ((1 + (AER/100))^(1/payment frequency) -1)

This is the same as I calculated from first principles, albeit I didn't express the AER and gross rate as a percentage so didn't have the multipliers of 100 in the equation. You'd only take the 365th root if interest was calculated and paid/compounded daily. ICICI calculate interest daily but pay monthly.

If interest is not compounded the percentage earned per period is simply (gross rate per annum / number of periods per annum), e.g. 1/365th of the total interest is earnt per day.

I hope my explanation is clear - its not the easiest thing to explain...

charlieboycat

You'd only take the 365th root if interest was calculated and paid/compounded daily. ICICI calculate interest daily but pay monthly.

I agree with Pagan98.

I'm not familiar with the expression "365th root", but the only time I've come across interest compounded daily (albeit not credited daily - ie. the daily interest is calculated on the balance plus accrued but uncredited interest) is Egg.

Everyone else seems to quote a gross monthly rate (circa 0.1% less than the AER) on their website and then use that rate simply divided by 365 and multiplied by the number of relevant days. Much easier to check!

isasmurf

ICICI quote the gross interest rate as 5.27%, and 5.03% from 1/11.