A&L Direct Saver Interest Question

WeatherMan

Hi folks,

I know there have been lots of threads in the past about formulae for compound interest questions, and i have looked through them, but not found the answer to my question.

I have an A&L Direct Saver account which puports to have an AER of 6.3% and a monthly compounded (annual) of 6.13%.

For the month of September i made no additional deposits and the interest rate did not change throughout. Hence i thought it interesting to check the calculation of interest.

Assuming that on the 1st of September i had £6747.26 (which includes the interest from August, added on that day). On the 1st of October i had £6774.38 i.e. gross interest £33.90, tax paid £6.78, net interest £27.12.

Ok. I tried to show that this was true. For this i would need the nominal rate of interest paid per month, call this D

(no compounding effect as only for one month)

Assumed d would be the gross rate /12 then taxed. I.e.

D = (6.13*0.8)/12= 0.4086666666 %

or as a fraction d = 0.0040866666666

applied to my account this would give me 6747.26 * d = £27.57

I.e. nearly (but more than) what i got £27.12.

Ok, thought i, maybe this is because the month is 30 days long (and some months are 28,31 days long). So i did it for the 30 day September:-

d=(6.13*0.8*30)/(100*365)=0.0040306....

implies interest would be £27.19.

I.e. Better, but still 7p off,

Now i'm a tight fisted sod, so though i'd try and account for the 7p.

Maybe the gross rate (6.13%) isn't exact i thought. Maybe they calculated it from the AER (6.3%) and it was then rounded for presentation purposes?

I tried to calculate the monthly Gross rate (G) from the AER (which i assumed to be true at 6.3%).

Rearranging the compound interest equation (allowing for different length months 7*31, 1*28 and 4*30) gave me:- (using taxed fractions here for ease)

annual rate = (1 + G*(31/365))^7 * (1 + G*(28/365)) * (1 + G*(30/365))^4 -1

which i then rearranged and solved iteratively for G using newton method. All calculations were done to double precision.

This produced a monthly gross rate which wasn't in agreement with the values seen either. (i won't go into much detail as i proved wrong - and i am not sure about the equation definition, although the proccessing was correct).

Can anyone help me with this?

I.e.

1. why did i get 7p less than my calculation above?

2. If the AER is correct then how do i use to get monthly rate (if my equation above is wrong).

3. Anything i'm missing?

Cheers,
WeatherMan

hereford_2

Not sure its that complicated.

If I remember rightly (I have a direct saver account too) they calculate interest daily, but only add it monthly.

Therefore at 6.13% gross interest divide this by 365 to get interest % per day, and further by 100 to turn it into a decimal fraction

6.13/(365 * 100) = 1.6794520547945205479452054794521e-4

30 days in septmber gives 30 * 1.6794520547945205479452054794521e-4 * £6747.26 which is £33.9951.

However what I think they've done is to calculate the interest on a daily basis to the nearest penny.

Interest per day is 1.6794520547945205479452054794521e-4 * £6747.26
which is £1.1331699 etc , which they've taken as £1.13, and 30 days at £1.13 is £33.90.


I suppose they don't deal in fractions of a penny. I wonder if they ever round up or always truncate.

I guess the only adding at the end of a month is also why the AER never works out with the gross by assuming the gross daily rate is compounded over 365 days, because it isn't with interest only added 12 times a year.

GCH888

Wasn't this the plot for Superman III where Richard Pryor diverted all those rounded down pennies into his wage check?

Is there perhaps a low-level A&L IT technician driving around in a red Ferrari even as I'm typing this?

YorkshireBoy

2008 is a leap year...

£6747.26 x 6.13% / 366 x 30 = £33.90

WeatherMan

Hi everyone,

Thanks for all for their helpful replies.

In response to Hereford and YorkshireBoy's replies.

I understand the calculation now.

Either A&L:-

1. Truncate interest per day to the nearest penny (tightfisted)
2. Round in to the nearest penny (no evidence as yet - but more equal)
3. Assumed September 2007 was part of the year including Feb28th 2008 so used 366 days.

Which one/ones is.are the truth?

I'm pretty happy with the leap year (say April to April includes Feb28th). Rounding seems fair, but truncating daily interest can add up!

WM

LittleVoice

YorkshireBoy is correct.

Truncating interest daily cannot be the case.

One has to assume they use the same process for calculating interest on this account as they do for any other.

If they were to use a truncating method, they would never pay interest on small amounts because the daily amount would never amount to anything.