Bank miscalculated interest due at end of fixed rate investment - Lessons learnt?

SnowMan

TheTelltaleChart said:

SnowMan said:

I agree that the daily compounding method will give less interest than the compounding when credited method on average. But it won't always do. See this example.

Agreed (I got there in a later post).

Your example shows daily compounding paying more interest when there is a higher balance earlier in the period, lower later on. If it were the other way round  — lower balance earlier, higher balance later — then daily compounding would give less interest. So this part can go either way.

Changes in the AER work differently, in that they will always lead to daily compounding paying less interest than compounding when credited.

Another one that causes real differences is if the account pays annual interest and the account is closed after 6 months before the first interest payment, or the first annual interest payment is on a fixed date after 6 months. The compounding when credited works in your favour here.

roose0

TheTelltaleChart said:

SnowMan said:

The gross interest estimate of £10.28 has been calculated using the formula

=IF(G18="Y",I17*(1+H17)^((A18-A17)/365.25)+C18-D18-J18," ")

Your use of 365.25 days in a year has already been discussed. The other thing that strikes me is that you're compounding interest daily. That's how I originally assumed it should be done, but when I looked at deposit takers' descriptions of how they calculated interest (which I admit I haven't bothered to do recently), they all seemed to compound only when interest is actually credited.

Mathematically: how much interest is accrued overnight, if the starting balance is B, the accrued interest since the last interest payment is A, the interest rate is R%, and there are Y days in a year (e.g. 365.25)?

With daily compounding, it's:

(B + A) * ( (1 + R/100) ^ (1 / Y) - 1)

With compounding when interest is credited, it's:

B * R / 100 / Y

(Noting that R is not necessarily the same in the 2 formulae: in the first formula, it's the AER, as you specified; in the second, it's the contractual interest rate, which differs from the AER when interest isn't credited annually.)

Daily compounding is generally going to give less interest than compounding when interest is credited.

To clarify, this is not a daily compound interest formula. A18 and A17 were a month apart. The expression "(1+H17)^((A18-A17)/365.25)" attempts to convert the AER to a gross rate. However, in reality, banks usually set monthly gross rates to a fixed value, regardless of the number of days in the month.

It is just a terminology issue, as your illustration below is correct.

SnowMan

Just to put this all into context. This is what the respective interest (paid and accrued but unpaid) looks like using the compounding method used in my checks and the traditional method used by savings institutions, on a lump sum amount saved of £10,000 over 5 years with interest paid annually at a constant 5% AER on the savings anniversary.

That's why I use the approximation in my spreadsheet. In this case the maximum difference (not visible on the chart because of its small size) is about £3 in interest. 

Using 365 or 365.25 days has about a 35 pence difference over a year.

If we look at what it would look like if the AER was 300% (we wish) over one year this is the result. The same thing is happening in the 5%pa example it's just that the curvature of the compounded line is too small to see in that case