How is daily interest calculated?

Robert_Sterling_3

If your method was really being used you would have half of the interest half way through the year.

OK Take the money + interest out

Put it back in

You now have more capital than in the first half of the year

So you will earn more interest in the second half of the year
.....................................................................................

What really happens is that the actual interest on the existing balance is added daily to the capital and thus the capital is increased day by day and the interest for the day increases every day.

Half way through the year you have less than half of the annual interest.

I kid you not.

Robert_Sterling_3

Stompa wrote: »

How the calculation should be performed though depends not only on how often the interest is calculated, but also on how often it is compounded.

It is calculated and compounded on a daily basis.

Robert_Sterling_3

It is better to get 3% half yearly than 6% per annum.

The Nationwide Building Society has a Smart Account for children. It pays interest half yearly.

Stompa

Robert_Sterling wrote: »

It is calculated and compounded on a daily basis.

In which case using the 365th root of 5% is the correct method.

Robert_Sterling_3

The 365th root of any number is very close to 1

So the 365th root of 5% i.e. 0.o5 is close to 1

What we deal with are multipliers

5% per annum gives you a multiplier of 1.05

After a year you multiply the original capital by 1.05 to get the new capital

To get the daily multiplier you extract the 365 th root of 1.05

to get the daily interest You start with the current capital
Apply the daily multiplier to get the new capital

Then subtract the old capital from the new capital

:j :j :j :j :j

rb10

Robert_Sterling wrote: »

It is calculated and compounded on a daily basis.

Ah! This is why our figures differ. Surely in most accounts, interest is calculated daily, but only compunded when it is paid?? So you don't earn interest on interest that has been accrued but not paid. That is what I based my figures on.

Robert_Sterling wrote: »

It is better to get 3% half yearly than 6% per annum.

If you take my way of working it out (assuming interest payments are exactly 1/2 way through the year), you get:
3% half yearly (i.e. 6% gross paid half-yearly) = 6.09% AER > 6% AER/gross paid annually.
So, as you say, 3% half-yearly is better than 6% p.a.

If you take your way of working it out, then 3% half yearly = 6% p.a., as if interest is compounded daily it makes no difference whether it's actually paid half way through the year or not, as the balance is still including that amount for interest purposes.


Isn't this the reason why most, if not all, other accounts that pay interest monthly or half-yearly will have a difference between the gross and AER? As the interest is compounded at stages during the year, it results in a higher AER. If it was compounded daily, there would be no difference between the gross and AER, as each would have equal compounding.

Robert_Sterling wrote: »

If your method was really being used you would have half of the interest half way through the year.

OK Take the money + interest out

Put it back in

You now have more capital than in the first half of the year

So you will earn more interest in the second half of the year
.....................................................................................

What really happens is that the actual interest on the existing balance is added daily to the capital and thus the capital is increased day by day and the interest for the day increases every day.

Half way through the year you have less than half of the annual interest.

I kid you not.

But your example above doesn't prove anything, because the capital that you have in the account for the second half of the year has increased (i.e. it's the original capital + the interest for the first half of the year). So you would expect to get more in the second half.

Sorry if I am being really thick, I just don't understand why what you are saying is true

Stompa

rb10 wrote: »

Surely in most accounts, interest is calculated daily, but only compunded when it is paid?? So you don't earn interest on interest that has been accrued but not paid.

AFAIK that's correct.

rb10

Stompa wrote: »

AFAIK that's correct.

Which makes my way of calculating it (using [gross rate]/365) correct, instead of the 365th root????

YorkshireBoy

I'm only aware of Egg who (say they) compound daily.

Stompa

rb10 wrote: »

Which makes my way of calculating it (using [gross rate]/365) correct, instead of the 365th root????

On the assumption that the interest is calculated daily and compounded annually, then yes. The OP didn't explicitly state how often interest was paid (i.e. compounded), but given that the gross and AER rates were the same it presumably must be annually.