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Annual Interest versus Monthly Interest?

Posts: 3 Newbie
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?

• Posts: 6,356 Forumite
If I invest £1000 with 12 monthly payments of £20...

This is £1000 + 12 months @ £20 = £1240, yes?

£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
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• Posts: 4,535 Forumite
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).
• Posts: 29,805 Forumite
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.
• Posts: 3 Newbie
Could someone explain this line of the calculation

£240 x [78/144th*] x 4.75% = £6.18

Where does the 78 come from?
• Posts: 171 Forumite
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.
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• Posts: 3 Newbie
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
• Posts: 332 Forumite
I would have to save the above threads for future reference. Who said you were too old to learn
-Keep your eyes to the sunshine and you would not see the shadows-:beer:
-Remember your forgetfulness is not my emergency
• Posts: 3 Newbie
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
• Posts: 1,654 Forumite
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).
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