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How do I calculate daily interest rates on savings?

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  • esbo
    esbo Posts: 462 Forumite
    Thanks everyone
    See if you can help me with this!!
    I'm having problems with the Halifax at the moment over the interest that they paid me when i closed the account, I think they have short changed me.
    I opened a 6 month fixed rate account that paid 5.19% net interest and invested 275,000.00 pounds. I opened it on 22/4/08 to mature 22/10/08 which works out 184 days, but I closed it early on 16/9/08, so I only had it opened for 148 days. Because i closed it early i lost 30 days interest on my money, which is fair enough that is the penelty for closing the account early, so i work it out that i should get 118 days interest. What they actually paid me was 3,369.56p, am i right in thinking that this is wrong, or maybe someone could explain to me how thay have worked this interest out, because for the life of me i can't work it out!!
    I have read all the small print on the terms and conditions for this account but could only see the part about losing 30 days interest.

    This is driving me nuts, someone help me please!!!!:confused:

    OK I will have a go at it, I will start with an approximation that 118 days is 4 months
    interest and see what that give me.

    OK month 1. initerest
    start 275,000.00 X 0.0519/12 ( 0.004325) = £1189.375 interest after one month, total=276189.375

    Well I can see where this is going, it looks like you only got 3 months interest, however it does not even seem to be that.

    OK month 2. initerest
    start 276189.375 X 0.0519/12= £1194.51 interest after two months, total=277383.885

    OK month 3 initerest
    start 277383.885 X 0.0519/12= £1199.68 interest after three months, total=278583.565

    So if we take the month 3 total 277383.885 and take the original 275,000.00 from
    it we have the total interest of £3583.565 which is more than the 3,369.56p they gave you, a shortfall of £214.005.

    So it seems you got less that 3 months interest at 5.19%.

    Now I am going to assume that the 5.19% was the AER and cacuulate the monthly
    interest rate from that, which come from formula b) in the notes from wikipedia.
    That comes to the (12th root of 1+0.0519 ) -1 =1.00422 or a rate of 0.422% a month

    So after 1 month the interest is 1161.98 total 276161.98
    So after 2 month the interest is 1166.89 total 277328.87
    So after 2 month the interest is 1171.82 total 278500.69

    That gives a total interest of £3500.69, which is still £131.13 short of what they gave you!!

    And that is really only 90 days interest not 118 days.

    So however they worked it out, even on the worst possible favourable method for you it is still short. So something seems very wroong there.

    On a side note, some time back, I wanted to pay my mortage off with a lump sum
    so I needed to see them to get an accurate value for the amount outstanding.
    However the figure they gave me was well off the value I calculated by about £1000, I questioned them several times about this because I did not want to pay it
    all off I wanted to leave a little outstanding. Anyway I worked out a value to leave some owning from their figure and paid that amount off.
    Some time after they sent me a check for about £800 or so saying I have paid off my mortgage completely and indeed overpaid (which I did not want to do!!).

    So I would definately have a word with them and ask them for a full statement showing the details of how that figure was arrived at and broken down into each
    monthly interest statement, because it seems even worse than the smallest amount you could possible calculate, even uning the least favourable method imaginable.

    I think you should also check your agreement regardiing partial months because
    they had your money for almost 4 months and they have not even paid 3 month
    worth of interest (90 days worth) under the poorest terms I can devise.

    Even things like waiting for you money to clear would make no difference because
    there is a buffer of 28 days.
  • Thanks for that
    I'm waiting for them to send me the breakdown of how they worked out the interest they've paid me. They told me in the Halifax that they work out the interest on a daily basis. and the interest on that account was fixed at 5.19%, so i basically worked it out by the amount of days it was in the account minus the 30 days loss of interest for closing the account early.
    It really is driving me mad, i can't wait to see how they have worked the interest rate out!!
  • Daisy:

    If you want the gross interest per day, the calculation is simple, just take the gross p.a. and take the 365.25th root of 1+gross

    If the gross interest rate per annum (AER) is i, (where 5% would be i = 0.05) then the interest per day will be ((1+i)^(1/365.25))-1.

    If you want to do 30 days of that, you'll have to compound it back again, it's easier to work out the 30 days gross interest, just do:

    ((1+i)^(30/365.25))-1.

    Multiply that by 100 to get percent if you wish.

    Don't forget to deduct 20% (or 40%) for tax to get NET.

    For example, if you have an account paying 5.19% gross pa then in 30 days you'll get 0.4164545% interest.

    Or, if you have £1000 deposited, you'll get £4.16 interest gross.

    which is £3.33 net after basic tax.

    Edit: seeing as you have said you have 275K, that works out at £1,145.25 gross per 30 days.
    Which is £916.20 after basic tax, or £687.15 after tax at 40% (But I don't think banks ever deduct the higher rate automatically, it's up to people to declare their own returns for this?)

    Edit: actually read your main post now. By my calculations 118 days interest would be

    £4,532.24 NET
    £3,625.79 After basic tax

    So it seems they've shafted you out a few days at least.

    Edit2: 16/09/08 - 22/04/08 = 147 not 148.

    It's critical what the 5.19% is though, whether it is net, gross or AER.
  • Daisy:

    If you want the gross interest per day, the calculation is simple, just take the gross p.a. and take the 365.25th root of 1+gross

    If the gross interest rate per annum (AER) is i, (where 5% would be i = 0.05) then the interest per day will be ((1+i)^(1/365.25))-1.

    If you want to do 30 days of that, you'll have to compound it back again, it's easier to work out the 30 days gross interest, just do:

    ((1+i)^(30/365.25))-1.

    Multiply that by 100 to get percent if you wish.

    Don't forget to deduct 20% (or 40%) for tax to get NET.

    For example, if you have an account paying 5.19% gross pa then in 30 days you'll get 0.4164545% interest.

    Or, if you have £1000 deposited, you'll get £4.16 interest gross.

    which is £3.33 net after basic tax.

    Edit: seeing as you have said you have 275K, that works out at £1,145.25 gross per 30 days.
    Which is £916.20 after basic tax, or £687.15 after tax at 40% (But I don't think banks ever deduct the higher rate automatically, it's up to people to declare their own returns for this?)

    Edit: actually read your main post now. By my calculations 118 days interest would be

    £4,532.24 NET
    £3,625.79 After basic tax

    So it seems they've shafted you out a few days at least.

    Edit2: 16/09/08 - 22/04/08 = 147 not 148.

    It's critical what the 5.19% is though, whether it is net, gross or AER.


    The 5.19% is NET interest, I only ever want to know what I will get after paying basic tax (20%).

    Thanks
  • The 5.19% is NET interest, I only ever want to know what I will get after paying basic tax (20%).

    Thanks
  • In that case, 5.19% net is 6.49% gross.
    It looks like you've received 88 days interest at that rate.

    That would correspond to a 60 day penalty.
    Amount            £275,000.00    
            
    Days            88    
    Net Rate        5.19%    
    Gross Rate        6.49%        Net Rate*1.25
            
    Interest in No of Days    1.5260%        ((1+Gross Rate)^(Days/365.25))-1
    (Gross)        
    Gross Interest        £4,196.38    Amount*Interest in x days
    After Tax        £3,357.10    Gross Interest*0.8        [FONT=Courier New]
    [/FONT]
    


    If we assume that the account was always 6.5% gross and only roughly 5.19% net then £3363.42 for 88 days.
  • Richard, I don't understand your post. I've looked at Halifax's website and they seem to display AER, then gross per annum then net for their fixed rate deals.
    You seem to say gpa and AER are the same thing:
    If the gross interest rate per annum (AER)
    As this is a 6 month deal, working backwards, I'd have thought
    gross per annum is 5.19/0.8= 6.4875%
    The AER from this would be ( 1 + 0.064875/2)^2-1=0.0659 ie 6.59%
    So they are not the same.I don't think AER is needed however.

    I would not use the AER here but merely the daily rate from the gross per annum rate ie 1/365th of 6.4875% if banks calculate interest daily.
    Why are you doing 365th roots?

    My method would then give an interest payment in agreement with posts further up:
    275000*117/365*0.064875*0.8= £ 4575.02 ( daily rate £39.10)
  • Well Daisy, you have given us all food for thought here.
    I’ve been thinking this over since this morning.

    I think I now see why Richard was taking the 365th root ….(1+a)^(1/365.25)-1 would give a daily interest rate if a is the AER,
    except I don’t think either 5.19% or 6.4875% are the AER.
    Unless Daisy corrects us, if 5.19% is the given net rate based on interest being paid at maturity of a 6 month term, I think that would produce an AER of 6.5927%.

    So here’s where I’m really confused now. Ordinarily, as said in my last post, I used to quite merrily just take 1/365th of the gross per annum rate (6.4875% here).
    When applied to 117 days gives:


    275000*117/365*0.064875*0.8= £ 4575.02

    Using the 365th root method , I get:

    275000*[1.065927^(117/365.25)-1]*0.8= £ 4545.62

    A difference of £29.40

    Not huge but significant enough when trying to work out accurate figures.( and nothing like Daisy's payment)

    How do banks calculate daily interest then? 365th root method or from gross per annum?

    Edit:
    LOL. After all that, I think I've come full circle. The root method would only apply if interest was paid out and compounded on a daily basis which it's not....
    so gross per annum is the way to go. People agree? I didn't realise my maths was quite so rusty until this thread. Thanks Daisy:mad:

    So for what it's worth, I think you should have received £4575.02 ie some 30 odd days interest adrift.
  • Thanks everyone

    I can't wait to see the explanation from the halifax, like I said I'm not very good when it comes to maths, but I'm sure that they have gone wrong somewhere, either that or they are changing the rules to suit them without letting the customer know. I wonder if anyone else has had a similar problem with this bank?
    I'll let you know the out come, watch this space!!!!!!

    I've copied and pasted part of the Halifax's term and conditions were it says about closing the account early, maybe someone could shed some light on the subject!!


    32. Closing the account early
    If you need to withdraw your money before the
    end of the term, you can close your fixed rate
    option
    (as long as it has been open for three
    months). If you close early you lose an amount
    equal to six days’ interest for each remaining
    month or part month of the term you chose
    (minimum of 30 days). We will work this out at
    the rate at which we pay interest on your
    fixed
    rate option
    . We may take this amount from the
    interest we owe you on your
    account which we
    have not yet paid. If there is not enough interest
    that we have not yet paid we will take this amount
    from your
    account. You can ask us to pay the
    money in your
    fixed rate option into either a
    variable rate option which you hold or your
    Halifax or Bank of Scotland Current Account as
    long as it is registered with our online service.
    You may have to open a
    variable rate option to
    do this.

    I closed the account about 5 weeks early!! So i Lose 30 days interest plus the 5 weeks i closed early, am I right or wrong in thinking this?
  • Hi Daisy.
    I did read the T&Cs and saw that and agreed with you about the 30 days at the time ( being the minimum amount).
    This confirms the product ie fixed rate websaver.

    From memory, the rates around the time would have been around the 6.5-6.6 AER mark so that tallies with your 5.19 net figure.

    So I stick with my verdict of £4575.02 lol. Do let us know. I'm interested for one.

    I also read that they start interest on the second working day after the day of receipt of cheques (4.3)....not that that would account for another 30 odd days interest that seems to be adrift.

    LTSB are having trouble getting their interest correct on current accounts at the moment so who knows?
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