Calculating savings interest

Dziekanowski

I have a Nationwide e-Savings account which is advertised as paying 5.80% gross p.a./AER.

The account information page says "Interest is calculated daily and paid annually."

I would therefore expect £10,000 invested in that account for a year to be worth £10,580 (before tax) after 1 year.

However, using Nationwide's Savings Illustrator at http://www.nationwide.co.uk/nbsasp/illustrator/default.asp it tells me that the money would be worth £10,588.80.

Can anyone out there enlighten me on what calculation they think Nationwide are performing to arrive at this figure? I've just phoned them and, astonishingly, the call handler I spoke to wasn't able to tell me precisely how they calculate the interest on my account!

caliston

It can't be something like 2008 is a leap year, so in the next 12 months you get an extra day? I can't make it work either. Or perhaps a daily rate figure is what they use to calculate the interest and when compounded it doesn't come out to a nice round number (but is slightly more than you were expecting, so no-one complains).

SeanW

I think they are calculating a Monday 1st October 2007 to a Monday 6th October 2008, which seems strange, but comes out close!

ringers

I think(and I could be very wrong here)
But at the end of day 1 the Nationwide works out the interest earnt on your 10,000 at 5.8% and divides it by 365 to get the interest your money has earnt on that day. 580/365 = £1.58
This is then your money and is added to your account (although it doesn't show in your balance and you can't get at it)
The next day you earn a days interest on £10001.58 and so on every day through out the year.
On the anniversary date the total amount of the interest is added to your account.
This is compounding, i believe

YorkshireBoy

It looks like the calculator takes into account that there will be an interest payment paid (on the £10,000 initial deposit) on 31st March 2008.

The interest earned from 1st April to 30th September will then be calculated on the new balance (of around £10,290).

caliston

But by that principle I make:
Daily interest rate = 5.8%/365 = 0.015890411% = 0.00015890411
Daily increase factor 1+0.00015890411% = 1.000158904
Annual increase factor 1.000158904^365 = 1.05971011283983 = 5.971% increase
(that was with 50 digits of calculation precision, so it's not rounding errors)

If I take the 365th root of 1.058 I get daily increase factor = 1.00015447859753812405
Annual increase factor accounting for leap year = (daily^366) = 1.05816343835619532879 = 5.816%
which is close but not quite. (daily^365 = 1.0579999999 = 5.8% as we started with)

[was replying to ringers]

Milarky

YorkshireBoy wrote: »

It looks like the calculator takes into account that there will be an interest payment paid (on the £10,000 initial deposit) on 31st March 2008.

The interest earned from 1st April to 30th September will then be calculated on the new balance (of around £10,290).

A great reply - the result is spot on when 365 days are assumed (175 then 190)

( 1 + (175/365)x5.80% ) x ( 1 + (190/365)x5.80% ) = 1.058840

But there's a problem with that: unless you closed your E saver account one year from now you would not receive this interest - as the paying out date does not coincide with the anniversary.

Is there anything to stop the determined customer from closing an E-saver every month and opening it again I wonder? That will raise the return from 5.8% to 5.95%

Dziekanowski

Quick update.

Part of my riddle has been solved in that Nationwide have 'fessed up and admitted that their calculator is, erm, mis-calculating.

I dare say that were I of the inclination to push it far enough they may be forced to honour some kind of compensation or increased rate as a gesture of goodwill for misadvertising but the bottom line is that the rate is a plain and simple 5.80% AER and not 5.888% AER as the calculator suggests.

Cheers for the help anyway, folks.

CLAPTON

Dziekanowski wrote: »

Quick update.

Part of my riddle has been solved in that Nationwide have 'fessed up and admitted that their calculator is, erm, mis-calculating.

I dare say that were I of the inclination to push it far enough they may be forced to honour some kind of compensation or increased rate as a gesture of goodwill for misadvertising but the bottom line is that the rate is a plain and simple 5.80% AER and not 5.888% AER as the calculator suggests.

Cheers for the help anyway, folks.

who in nationwide confessed to error?

why do you doubt yorkshireboy/milarky results?

YorkshireBoy

Dziekanowski wrote: »

...astonishingly, the call handler I spoke to wasn't able to tell me precisely how they calculate the interest on my account!

Quite frankly I'm astonished that you're astonished that a call handler couldn't tell you precisely how they calculate interest on your account! At the end of the day though, the help files on the N/W site tell you how they do it...

• They calculate interest at 5.80%/365 on the closing balance each day.
• Your money only earns interest from the first full day it is in your account (I read this as the day after you deposit it).
• Interest is paid on 31st of March each year.

I dare say that were I of the inclination to push it far enough they may be forced to honour some kind of compensation or increased rate as a gesture of goodwill for misadvertising

Highly doubtful, because a) they say...

Important Information
This illustrator is designed to show approximately the total amount saved in a number of scenarios. The amount displayed is for illustration purposes only.

...and b) if you opened the account on 1/10/07 and closed it exactly one year later, you would actually receive an amount of interest equivalent to an AER of 5.888% as Milarky and I demonstrated earlier.

the bottom line is that the rate is a plain and simple 5.80% AER and not 5.888% AER as the calculator suggests.

The calculator doesn't "suggest" anything with regard to AER. It clearly says that the rate payable is 5.80% AER. It then illustrates what interest amount you'd receive under a given set of circumstances, which again they clearly detail.

Dziekanowski

CLAPTON wrote: »

who in nationwide confessed to error?

why do you doubt yorkshireboy/milarky results?

The person who confessed to the error was the person who maintains the part of the website which performs the calculations. A fairly authoritative source, I'd have thought.

Why do you doubt what I am saying? Feel free to call them yourself between 9 and 5 on a weekday and ask to be put through to the department that performs interest calculations - that was how I got to talk to someone in the know. They seemed bemused when I explained what I was seeing and they promised to call me back later this afternoon once they understood what was happening. The person I dealt with was called Lucy.

Sure enough, they called me back and said that it was an error on the website which they were looking to fix without delay.