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  • FIRST POST
    herraghty
    Annual Interest versus Monthly Interest?
    • #1
    • 5th Sep 04, 4:26 AM
    Annual Interest versus Monthly Interest? 5th Sep 04 at 4:26 AM
    This is a hypothetical question which I would like to know the answer to:

    For a savings plan, is better to have interest added annually or monthly?

    If you know the answer then could you confirm my calculations?

    If I invest £1000 with 12 monthly payments of £20 at a rate of interest of 4.75% for 1 year then I calculate that if interest is added annually I would get £1,298.90 and if interest was added monthly then I would get £1,294.81

    Does anyone agree with my calculations? Should I receive more or less with the monthly plan?
Page 1
  • Milarky
    • #2
    • 5th Sep 04, 10:08 AM
    • #2
    • 5th Sep 04, 10:08 AM
    If I invest £1000 with 12 monthly payments of £20...
    This is £1000 + 12 months @ £20 = £1240, yes?

    Interest of 4.75% added annually:

    £1000: + £47.50 = £1047.50

    £240 x [78/144th*] x 4.75% = £6.18

    Total £1240 + £53 68 = £1293.68

    Your figures are both higher, so you seem to have used a different method and/or different interest rate.

    In truth it shouldn't make any difference as long as the AER on two separate accounts [one paying monthly, the other at the anniversay] were the same.


    *assuming £20 is added !to account on 1st of each month, so that the final instalment goes in one month before the anniversary
  • Joe_Bloggs
    • #3
    • 5th Sep 04, 1:11 PM
    • #3
    • 5th Sep 04, 1:11 PM
    It might make sense to be paid monthly so that you can ditch savings institutions that don't keep up with rate rises and take your interest earned and capital with you to invest in other ways. Annual interest and breakfast is for wimps. Give me monthly interest any time of the day.
    J_B (AKA Gordon Gecko).
  • lisyloo
    • #4
    • 5th Sep 04, 2:09 PM
    • #4
    • 5th Sep 04, 2:09 PM
    Annual interest and breakfast is for wimps.
    I don't agree with that.
    Cahoot at 5.65% are paying annually, so if you insist on being paid monthly (which is more expensive for the lender in admin) then you might have to sacrifice the best rates.

  • herraghty
    • #5
    • 5th Sep 04, 2:41 PM
    • #5
    • 5th Sep 04, 2:41 PM
    Could someone explain this line of the calculation

    £240 x [78/144th*] x 4.75% = £6.18

    Where does the 78 come from?
  • MJSW
    • #6
    • 5th Sep 04, 3:43 PM
    • #6
    • 5th Sep 04, 3:43 PM
    Where does the 78 come from?
    It's the number of months your £20 monthly deposits have earnt interest over. The first deposit earns 12 months, the next 11 months etc. 78=12+11+10+...+2+1.

    I agree with Milarky's calculation of the annual interest, although I disagree that having monthly or annual interest doesn't make any difference if the AERs are the same. This will only be the case where the deposit is left in place for a full 12 months. However in this case the balance won't be constant over the year and so there will be a difference (admittedly a very small one).

    If the balance in the account is increasing, then the total interest with annual interest will always be higher than a monthly interest account with the same AER (although the difference will be very small). This is because the AER calculation assumes the monthly interest will compound for a full year, but in practice it won't.

    In this case, the interest on the monthly deposits won't be in the account for the full 12 months. Interest on the very first deposit will compound for 12 months, but the second will only get 11 months, the next 10 months etc.

    For example, the balance (including interest) on the anniversary date on the first deposit would be £20x1.0475 with annual interest, or £20x(1.0475^(12/12)) with monthly interest, ie exactly the same. But on the final deposit, you end up with £20x(1+0.0475x1/12) annual compared to £20x(1.0475^(1/12)) monthly. These figures are not the same, the annual interest is greater. The annual interest will always be slightly higher (comes down to maths, but ax+by >= x^a+y^b if a and b are between 0 and 1. Here we have x=1.0475,y=1,a=1/12,b=11/12.)

    Another factor is tax. If you are a taxpayer, you will be better with annual interest. This is beacuse tax is paid earlier with monthly interest, and so you don't get the full benefit of compounding on the gross interest which the AER calculation assumes. If you are a higher rate taxpayer, then this difference becomes even greater since your some of the interest may become payable in an earlier tax year, accelerating the additional 20% higher rate tax liability by a further 12 months.

    Also, any changes in the interest rate (either up or down, doesn't make any difference) will always leave you slightly better off with annual interest compared to monthly. Again this is down to maths, and the inequality above.

    Overall, based on the figures you provided, you would receive interest of £42.94 (after tax) with annual interest, or £42.73 with monthly interest, a reduction of 21p.
  • Judi
    • #7
    • 5th Sep 04, 11:21 PM
    • #7
    • 5th Sep 04, 11:21 PM
    ??? ??? ???
  • herraghty
    • #8
    • 5th Sep 04, 11:25 PM
    • #8
    • 5th Sep 04, 11:25 PM
    Thank you all very much.

    Especially Milarky for the original calculation and MJSW for the in depth explanation.

    I'm sure a few people (including myself) learn something.

    Thanks
  • Bleg
    • #9
    • 10th Sep 04, 6:07 PM
    • #9
    • 10th Sep 04, 6:07 PM
    I would have to save the above threads for future reference. Who said you were too old to learn
  • bigwoman
    I have £25,000 lump sum to invest. I want to invest it in a way that pays me interest monthly as Iam low paid and this will help towards my bills. Can anyone tell me the best place to invest it and what monthy return i can expect to recieve
  • david78
    I disagree with the arguments being made here, especially the one that says you lose out on compounded interest if you are paid net interest monthly. No wonder poor Judi is confused!

    All that matters is the AER. Two accounts with the same AER (one paying interest monthly, one annually) will both pay out the same net interest and will both pay the inland revenue the same tax provided the interest is retained in the account. They are "Equivalent".

    When you get interest monthly, it is not correct to say that 20% tax has been taken from each gross monthly payment. Just enough tax is deducted so that the amount compounds and adds up to 20% tax for the year as a whole. This is why with savings accounts which pay interest monthly the tax is not included on monthly statements, but is only shown on your annual statement (usually sent out after the end of the tax year).
  • david78
    bigwoman,

    Very roughly, £25000 invested at 4% net (5% gross) should give an income of about £83 per month.

  • Judi
    No wonder poor Judi is confused!
    Beleive me, it doesnt take a lot!!!

    Very roughly, £25000 invested at 4% net (5% gross) should give an income of about £83 per month.
    Blimey its not a lot is it? Some poor sod has slogged his guts out to earn that £25000 to get a measly £83 a month interest.

    The reason i like monthly interest added to my savings is because i like to see how much interest i am gaining per month. I keep thinking i ought to put it in a higher interest account but i cant work out the interest that would have accrued (blimey where did that word come from? ) on a monthly basis. Is there a calculation that would help me so that i wouldnt lose heart?

  • Joe_Bloggs
    It is so easy to fritter money away with bank charges and interest rate charges that can rival 25K of savings interest for a month.

    (blimey where did that word come from? )
    According to the beeb it came from God Blind Me to Cor Blimey etc. The referenced site mentions asterisked out swearwords.
    http://www.bbc.co.uk/dna/h2g2/A753527
    J_B (At yer service ma'am)
    PS It's accrual world in the savings business.
  • Milarky
    But Judi's observation shows the 'logic' of keeping the interest on OPM ('other peoples' money) via 0% credit cards - opps other board!

    In an ideal world, we wouldn't have any 'savings' just huge amounts of borrowed money on which we earned a bit of the interest.

    Now the fact that the current 'bit-rate' is only about 4% after tax (0.25% per month) at best is surely a reflection of the other fact which cannot have escaped our notice, which is that banks have so much money that they have to 'pay us' to take it, so to speak..

    It's better to be earning a poor return on OPM, than am 'honest buck', surely? This way, if you need more income just 'borrow' more money at any rate less than 4%... ;D

  • david78
    Totally agree. We should be making as much interest on our savings as we can and making as much interest on other peoples money as we can.

    Not sure what formula Judi is looking for. If you open an account which pays interest annually, the interest you expect is:

    amount on depost X 0.8 X interest rate in % / 100

    X = times
    / = divide.

    If you want to get a very rough idea of how much is accruing per month just divide by 12.
  • Judi
    Not sure what formula Judi is looking for. If you open an account which pays interest annually, the interest you expect is:

    amount on depost X 0.8 X interest rate in % / 100

    X = times
    / = divide.

    If you want to get a very rough idea of how much is accruing per month just divide by 12.
    Thats what i wanted to know. Thanks David.
  • MJSW
    I fear Judi may become even more confused once she's read this! !;D

    All that matters is the AER. Two accounts with the same AER (one paying interest monthly, one annually) will both pay out the same net interest and will both pay the inland revenue the same tax provided the interest is retained in the account.
    Sorry this is wrong. It is only the gross rates that compound to be equivilent. This is comfirmed by the definition from the British Banking Association: "The Annual Equivalent Rate is a notional rate quoted in advertisements for interest-bearing accounts which illustrates the contractual (gross) interest rate (excluding any bonus interest payable) as if paid and compounded on an annual basis." (from http://www.bba.org.uk/bba/jsp/polopo...135&a=1575 )

    It is mathematically impossible for both the gross and net AERs for the monthly and annual accounts to be the same as each other (unless either the tax rate or the interest rate is 0%). If the gross AERs are the same, the net AERs have to be different. The net rate will always compound to slightly lower figure. I have a first class degree in mathematics, and would be very interested to see your calculations if you believe that the net AERs can possibly be identical at the same time as the gross AERs being identical.

    The other thing you need to understand is the circumstances in which the rates will be equivilent. Because of the way an AER is defined, they are only equivilent if the the money is left intact for 12 months, and the balance never increases or decreases (apart from the interest credits). I shall demonstrate this with a simple ( ! ) example (I've ignored tax). Suppose A opens an annual interest paying 5% annually on 1 Jan 04. B opens a monthly account paying an an AER of 5%, which makes the monthly rate 4.89% (figures derived from ING). If both deposit on 1 Jan and leave the money to compound gross for 12 months, then the final balances will be the same. But suppose both put £0.01 in there for 11 months, and then at the start of month 12 deposit £99,999.99 (extreme example I know, but it illustrates the point!).

    In month 12, A earns £100,000x5%x1/12=£416.66.
    In month 12, B earns £100,000x4.89%x1/12=£407.50.

    Interest is added to both accounts on 31 December (being the end of the year for A, and the end of the month for B). On that date A, has a balance of £100,416.66, but B only has £100,407.50. Essentially B has lost out on his compounding. If the money is in place for a year, B is compensated for his lower rate by the monthly compounding. But in the example above, he has received no compunding because he received no interest on which to compound during the first 11 months. So the rate, which were apparently equivilent, are in fact not equivilent.

    It is a common misconception that annual equivilent rates are always equivilent - they are not (as the example demonstates). The monthly and annual interest will generally only be identical if:

    1) The interest rolls up gross, and
    2) No deposits or withdrawals are made from the account, and
    3) Interest on the annual account is paid 12 month after the opening date (if it is paid sooner, then again annual will beat monthly).

    Otherwise the figures will be different, although I stress again the differences will usually be relatively small and unlikely to be worth worrying about. By the way, I'm not necessarily saying than monthly interest will always be worse than annual interest. There are circumstances in which monthly interest will work out better (generally where the balance is reducing over the year).

    When you get interest monthly, it is not correct to say that 20% tax has been taken from each gross monthly payment. Just enough tax is deducted so that the amount compounds and adds up to 20% tax for the year as a whole.
    Really? Perhaps you should tell the Inland Revenue so that the bank in question can be prosecuted! When a bank or building society pays interest it is obliged to deduct lower rate tax under ICTA1988 (unless it is an ISA or the saver has registered for gross interest). If they deduct either more or less than 20% (subject to rounding to the nearest penny) they are breaking the law. Can you give me a single example of a bank which has deducted less than 20% on a monthly interest payment? !Do you have any links to any websites which confirm that banks use this procedure?

    In any evernt, it would be mathematically impossible to adjust the tax deducted from monthly interest as you describe. The only way this could be achieved is by deducting no tax at all from the monthly interest and paying it all at the end. Unless the full gross payment is credited to the account each and every month without any deduction of tax at all, then it is a mathematical certainty that the net balance after 12 months will be lower than with annual interest (although as I said before these differences are very small). In fact you would pay slightly less tax with monthly interest (because you would earn slightly less interest).

    This is why with savings accounts which pay interest monthly the tax is not included on monthly statements, but is only shown on your annual statement (usually sent out after the end of the tax year).
    All the monthly interest accounts I have, apart from Ing, show the tax deduction every month, and it is always 20%. Even with Ing you can even track the gross interest, as the statement tells you the gross interest earnt in the calendar year to date. If you deduct the net interest credited to the account in the same period, that gives you the tax deducted to date. This will be 20% of the gross interest.
  • Joe_Bloggs
    @MJSW
    I'm glad that the bba link was only a partial illustration
    to AER and not the complete explaination.
    How does one compare an AER on a monthly interest paying account with an AER on an annually paying interest account ? The comparison is at the end of the first year, !assuming the same initial deposit of capital and no interest is withdrawn on the monthly account. Neglecting tax of course. If it's a few tens of pence in a £1000 then don't bother.
    J_B.
    PS The interest on many accounts is calculated daily and the net results displayed monthly.
    ! ! ! ! !
  • Judi
    Ok. maybe it would be easier if i asked how much interest a month i would get with £1500 at 5.50% ???
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