Santander - Interest out by 5p

mgarl10024

Hi,

I know this is a little sad, but once again, I just can't get my interest to add up. I'm quite happy to believe that it's me, and I just want to get it right in my head because I'm trying to learn, not because I am losing sleep over 5p. :-)

I have a Santander Preferred Current Account which pays 5% AER. So, that is 4.89% gross using the calculations here (well, 4.88894854038%)
http://forums.moneysavingexpert.com/showpost.php?p=5537885&postcount=3

My Statement says "23rd Jan to 21st Feb".
On the 23rd of Jan, I had £1,012.50 and Santander paid me £2.18 interest for the previous month. This made the balance £1,014.68 for that day.
I then topped up the balance to £2,500 for the remainder of the month.

As I work it, I should be paid 1 day at £1,014.68, and from the 24th Jan - 21st Feb (29 days) at £2,500.

So,
0.0488894854038 (gross annual rate) / 366 days x 1014.68 x 1 day = £0.1355387515
0.0488894854038 (gross annual rate) / 366 days x 2500 x 29 days = £9.68439259973

£0.1355387515 + £9.68439259973 = £9.81993135123

£9.81993135123 * 0.2 = £1.96398627025 tax or £1.96 tax.
£9.81993135123 - £1.96398627025 = £7.85594508098 or £7.86 in my hands.

Santander paid £7.81 having deducted £1.95 tax.

Anyone see where I've gone wrong?

Thanks,

calypso_rhapsody

I don't know for sure but i would think that it is because interest is calculated daily and Santander don't run to quite so many decimal places each day as you do. So in the rounding you may find that it's 5p out over the month.

I did also wonder if it might be the time to clear the transfer in - but i think that would make a bigger difference.

I haven't checked the arithmetic in your calculations but your approach looks right to me ...

ajbell

Its not an answer to your question but wouldn't interest be calculated on a 365.25 day year?. Average is actually 365.249 days.

Linton

Strictly speaking your calculation method is wrong:

Assuming 366 days in year:

Gross interest rate for 1 day= 1.05^(1/366)-1=1.000133315
Gross interest rate for n days = 1.000133315^n - 1

It makes less than 0.1p difference, so doesnt solve your problem.

mgarl10024

Linton wrote: »

Gross interest rate for 1 day= 1.05^(1/366)-1=1.000133315
Gross interest rate for n days = 1.000133315^n - 1

It makes less than 0.1p difference, so doesnt solve your problem.

Are you sure that you are not confusing this with daily compounding interest? I only get interest once a month.

psychic_teabag

Doesn't that assume that the interest compounds daily. But if the interest is calculated on the balance, it wouldn't compound until it's actually credited. (?)

mgarl10024

ajbell wrote: »

Its not an answer to your question but wouldn't interest be calculated on a 365.25 day year?. Average is actually 365.249 days.

I couldn't get the last statement to add up, because I was using 365 days. When I went to 366 (leap year) it worked, so I assumed that was right.

If anything, reducing the number of days means that the daily rate goes up, and so the difference increases! I need about 369 days this year to agree with Santander.

Linton

My answer is mathematically pure but, yes, it does seem that banks dont work that way. For example the coop says that it works out daily interest using the approach adopted by the OP, though it doesnt say whether it uses 366 days for leap years. I couldnt find any statement from Santander how they calculate interest.


Interesting (well sort of).

CKhalvashi

You’ve got a very bored Maths graduate going through this. Yes, you have the maths completely correct and Santander have probably rounded down to preserve their £11bn profit

VK

Thrugelmir

How did you deposit the additional funds into the account?

mgarl10024

Thrugelmir wrote: »

How did you deposit the additional funds into the account?

It went through as a Bill Payment (it was from another Santander account, in another name). I believe it went through Faster Payments - as the source account shows the same date as this account for the transaction.