Annual Interest versus Monthly Interest?

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

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.

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.