AER vs Gross interest

Robert_Sterling_3

tomstickland wrote:

All of this works because of the approximation
(1+a)^b = 1 + ab which is true when a is small (and 0.05 is considered quite small).
.

".05 is considered quite small."
.05 times a million pounds is £50,000!


If you want accuracy to the nearest penny on loand exceeding £10,000 then you need accuracy to 7 significant figures.

tomstickland

Yes, but the error introduced as a result of using the expansion was shown to be

For an average month with n=30 then those two methods agree within 0.0008%

0.0008% of a million pounds is £8.
Still not insignificant.

Doesn't Excel have some well know rounding error that could effect this?

isasmurf

lipidicman wrote:

In response to ISAsmurf the only time you can do x%/365 is if the rate is a gross rate paid daily (just as you can do x%/12 for a gross rate paid monthly. You then raise this result to the power of 12 to get the AER. This explains why the AER and the gross rate are different for monthly interest)

You better explain to ING Direct then that they are calculating the interest wrongly.

lipidicman

Isasmurf. ING indeed have it correct because they compound monthly. So the Gross rate is based on a month and doesn't account for compounding. So it is valid to divide the gross rate by 365 to get a daily rate (as the period is smaller than the compounding period). So I was slightly wrong above. You can divide the gross rate by any period that is smaller than the compounding period. However with the AER you must raise it to a power to get to the 'daily-rate-as-if-it-was-compounded-daily'! confusing!

However the best plan is to look at the AER to remove the effects of whether a bank compounds daily, weekly or annually. This will tell you the amount of money you will get!

Nick_C_4

So do ING pay the same interest rate per day in different months, and different rates per month? Or the same rate per month and different rates per day?

e.g.

monthly_rate = gross_pa/12, daily_rate = monthly_rate/days_in_month

OR

daily_rate = gross_pa/365 (or 366!), monthly_rate = daily_rate * days_in_month

It must be the latter....

Also, although they say they calculate interest daily, they almost certainly don't mean this literally. If they did, they'd have to process every bank account every day. The system I know calculates the interest every time the balance changes, and you don't actually have to do it more often than the interest is paid. All they mean is that interest is calculated based on the balance at the end of each day.

AER = (1 + gross_pa/freq)^freq - 1

where freq = # of times each year interest is paid

When interest is paid annually (i.e. freq = 1) then AER = gross_pa. The important thing is that gross_pa has to be quoted along with the frequency, while AER is independent of the frequency that interest is paid. That's why the FSA have insisted that it's used.

grumbler

Nick_C wrote:

monthly_rate = gross_pa/12, daily_rate = monthly_rate/days_in_month

OR

daily_rate = gross_pa/365 (or 366!), monthly_rate = daily_rate * days_in_month

It must be the latter....

I am sure the latter is correct.

...although they say they calculate interest daily, they almost certainly don't mean this literally. If they did, they'd have to process every bank account every day.

Indeed they do calculation once a month. What they say is that if, for example, balance is different every day, interst depends on daily balance, but not the final amount at the end of the month.

AER = (1 + gross_pa/freq)^freq - 1

where freq = # of times each year interest is paid

When interest is paid annually (i.e. freq = 1) then AER = gross_pa. The important thing is that gross_pa has to be quoted along with the frequency, while AER is independent of the frequency that interest is paid.

This formula is almost perfect, but not absolutely. What is frequency if interest is compounded monthly? Months are different. The absolutely perfect calculation in ING case for normal year is:
(1+0.0465/365*31)^7*(1+0.0465/365*30)^4*(1+0.0465/365*28)=1.047503869
For frequency 12 it will be:
(1+0.0465/12)^12=1.047503944

I know without calculations that the difference is very small and the latter formula can be always used, just want to make things absolutely clear ...

Nick_C_4

Yep, you're right, assuming that the interest is the same every day (and differs every month), which we both just agreed on. My formula would only be correct if the interest periods are equal.

al_yrpal

So does it pay to 'decide Nationwide'(e-saver), or is it best to go for 'no catches' at ING Direct - they both advertise the same rate of interest.

lipidicman

Nick_C wrote:

The important thing is that gross_pa has to be quoted along with the frequency, while AER is independent of the frequency that interest is paid. That's why the FSA have insisted that it's used.

Just wanted to quote that because that is exactly the point that I have been making. Its easy to remember and contains no formulas, for those of you that don't like them.

dixie_dean_2

Sorry to be lazy and maybe in the wrong post but...

If i put the max £250pm into the A and L 10% account, how much will I have after the 12 months?

Actually, I'm not sorry, otherwise I wouldn't have asked, but I'll definitely be very grateful if someone could help.

Cheers (even if nobody helps)