Interest Calculation

[fbg40]

Hi
Can somebody please explain how the interest is calculated when it is stated that the interest is paid daily ?
E.G.

What would the estimated balance be at the end of the 12 months based on 12 monthly deposits of £500 totalling £6,000?

The balance on 12 monthly deposits of £500 paid on the first day of each calendar month with an interest rate of 5.00% gross p.a./AER (variable) would be £6,162.50.

This estimated balance is for illustration only and assumes that:

Interest is paid into the account.
No further deposits or withdrawals are made.
There is no change to the interest rate.
Individual circumstances do not change.

The above illustration is from a well known Building Society, a similar account to mine where they state that the interest is paid daily.
Many thanks
FBG40

[Old_Geezer]

Without searching the Net I'd have no answer from my own knowledge, but it's likely to be a fancy algebraic equation: but APR is what you need for comparison purposes.

One wonders if they calculate further interest in February on the interest they paid in January.

[puzzlemaniac]

basically it's the 5% annual rate divided by 365 days.
on the first day that the deposit earns interest it will be £500 x (5/36500) so £0.0684p. If interest is paid daily then that very small value is added to the initial £500. On the next day, the calculation is based on the £500.0684 x 5/36500, and so on.

[Old_Geezer]

Surely, if they pay interest on interest then simply dividing by 365 will give a larger than 5% overall annual rate by the end of the year ? I can't help but feel that it must be a little more complex than that.

[fiction-factory]

Looking at your example if you pay 12 deposits of £500 over a year you have £500 for 12 months plus £500 for 11 months plus £500 for 10 months..... plus £500 for 1 month.

Over the year you have paid in £6000 and on average it has been in there for an average of (12+11+10+....+2+1)/12 months- ie for 6.5 months.

Over the year your interest on £6000 final balance is £6000 x 6.5/12 (as it has been there for 6.5 out of 12 months on average)

That gives £162.50 interest,. So the final balance is £6162.50

[fiction-factory]

Alternatively look at it like this. You have £500 at the start of month 1, £6000 at the start of month 12 and still have £6000 at the end The average balance over the year is £3250.
£3250 at 5% pa = £162.50

I wouldn't get bogged down with compound interest calculations. The AER must take account of this. You are getting 5%

[fbg40]

Many thanks for all the answers folks - very enlightening !
FBG40