Calculating Contractual Interest

So, we have The charges themselves all totted up. And we have the interest which we were charged on those charges all totted up. And now we have a spreadsheet with a load of money that the bank has taken from us a while ago. So we're going to claim that back, as they have effectively "borrowed" it from us without our authority (with no authority whatsoever, as it turns out !!) We could call this "nicked" perhaps, but let's be civilized and call it unauthorised borrowing. Now that rings a bell !!


So, we NOW charge them for having had this money from us all this time, by applying interest to this money at the rate specified in our contract with them. THIS - at last - is the contractual interest we have been wittering on about. So now we add interest to each and every penalty charge, AND each and every bit of interest that was charged on that charge. AND we add it at the current rate, NOT at any older rate - WE are charging them NOW - at the rate they are currently applying.

So - now we have:
1. The original penalty charges;
2. The interest we have been charged on those penalty charges ("DEBITED CI") ;
3. The interest that we are NOW charging the bank for taking those penalty charges from us ("ADDED or EXTRA CI") ;
4. The interest that we are NOW charging the bank for taking interest on those penalty charges from us ("ADDED or EXTRA CI").

And that is the sum total of our claims.

Hopefully that made sense.I suggest that the following is included in any court bundles for CI claims, as it should hopefully answer any questions the court may have concerning how the CI claim has been calculated:-


The claim consists of the following elements:
1. The original penalty charges;
2. The apportioned interest which HAS BEEN charged on those penalty charges;
3. The interest that the Claimant is NOW charging the bank for taking those penalty charges from their account;
4. The interest that the Claimant is NOW charging the bank for taking interest on those penalty charges from their account.

The interest that the Claimant is now charging is at the published contractual rate currently being charged by the Defendant for unauthorised borrowing.
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Information published online, regarding the various quoted interest rates.
From Smile.co.uk :-
[quote]
GROSS
Gross means the contractual rate of interest payable before the deduction of income tax at the rate specified by law.
AER
AER is the notional rate which illustrates the contractual interest rate as if paid and compounded on an annual basis.
APR
APR is the total charge for credit in line with regulations under the Consumer Credit Act 1974 and is used across the whole UK financial industry on the basis it allows you to compare the cost of different forms of credit (such as loans and credit cards). When an APR is calculated, certain fees and charges are taken into account.
EAR
EAR is the equivalent annual rate taking into account the interest rate and how often interest is paid but excludes any fees or charges.
[unquote]

From Intelligent Finance :-
[quote]
Current Account:

# If, without our agreement your current account goes overdrawn or you go over your overdraft limit, we will charge you interest on the amount you are overdrawn or the amount that is in excess of your agreed limit at our unauthorised overdraft rate.

* EAR is the Equivalent Annual Rate. If we agree to let you have an overdraft, we will decide your overdraft limit and tell you what it is. Overdrafts are repayable on demand.

** AER stands for Annual Equivalent Rate and illustrates what the interest would be if interest was paid and compounded each year. The gross rate of interest payable before the deduction of income tax at the rate specified by law is the contractual rate specified by law. The net rate is the rate of interest payable after allowing for the deduction of income tax at the specified rate (currently 20%).
[unquote]
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An explanation of the method of calculating EAR/APR rates.
Neither the EAR nor the APR rates are the annual rates actually used to directly calculate compound interest with. Unless the interest is simple, or is compounded annually (or longer), then the EAR or APR is higher than the actual annual rate used.

EAR:-
For a given amount (the Principal), of £100, interest at an annual rate of 20.00% compounded daily will amount to £22.13 after one year. The EAR rate is the interest added after one year, expressed as a percentage of the Principal amount. So the EAR in this example would be 22.13%. If, however, the interest rate being applied was 20.00% simple (or 20.00% compounded annually), then the total interest added would be £20.00 and the EAR would then be 20.00%.
APR:-
Normal Credit Card purchases - The same would apply to a credit card purchase of £100. Interest at an annual rate of 20.00% compounded daily will amount to £22.13 after one year. The APR rate will then be 22.13%.

Cash Advances:-
The difference between EAR and APR occurs when there are certain additional "one-off" charges made in relation to the amount in question, and the initial cash advance fee is one such charge. For a Cash Advance of £100, incurring a one-off fee of £2.00, the annual interest rate of 20.00% compounded daily REMAINS THE SAME. However, the Principal amount (for the purpose of calculating compound interest) becomes £102.00, so the interest at an annual rate of 20.00% compounded daily will amount to £22.58 after one year. The total cost of borrowing that £100 over the first year will have been the £2.00 fee, plus the interest of £22.58 = Total of £24.58. so the APR rate in this case will be 24.58%.

Thus, there is NO higher or lower (as in "unauthorised or authorised") rate of annual interest actually being applied to credit card borrowing - just one single annual rate. The apparent difference in rates is only existent in the APR rates, and is purely the result of the mechanics involved in adding the fee to the Principal amount, and not applying a higher rate.

Applying the standard formula for calculating compound interest to the EAR or APR rates, is therefore technically incorrect, and the original rate used to arrive at the EAR/APR rates should ideally be used.

[Simian]

Calculating Compound Interest

Now the maths !! I suggest the following is also added to any court bundle for CI claims. This may help anyone who may be using a spreadsheet of their own, and wants to enter their own formulae. It shows how the calculation of compound interest is carried out, and used in a spreadsheet:-

For calculating interest compounded daily, we have to calculate the daily rate r, and this is found by dividing the annual interest rate by 365.
We then add 1 to this figure to arrive at (1+r)
We then calculate the number of days elapsed since the charge was made to the date of calculation (eg today), which gives you n
We then raise the figure you obtained from (1+r) to the power of n, that is: (1+r)^n
We then multiply the Principal P by this figure to give P*(1+r)^n
So we do not just multiply (1+r) by n, we actually multiply it by itself n number of times.
Then we multiply that by P.
The result of this calculation will give the total amount owed (including the Principal P), so to work out just the interest charged, we subtract P from this final result.
However, if we are calculating this from an AER or APR rate, then we should first obtain the actual annual rate used in arriving at the AER/APR rate. This is actually a lower rate than the EAR or APR, and more accurately represents the banks' calculations.
The formula for converting the EAR/APR rate to the actual annual rate (where EAR is the EAR rate expressed as XX.XX%) is :
365*(((1+EAR)^(1/365))-1)

The two formulae above can be combined, to give a simpler single formula, which calculates the total payable (Principal + Interest) directly from the AER:
P*((1+AER)^(1/365)^n)
Again, subtracting P from this will give the actual compound interest charged.
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Entering the formulae into a spreadsheet.
For MS Excel sheets, calculating directly from the EAR/APR rate:-
Putting the formula on row 1 of the Excel spreadsheet exactly as:
"=B1*(1+(E1/365))^D1"
- where B1 is £100.00, E1 is 20%, and D1 is 365 days - gives £122.13
The mathematical hierarchy used forces it to use this set of priorities:-
The spreadsheet works out (E1/365) first, to give 0.000548,
then adds 1 to give 1.000548,
then raises this to the power of 365 to give 1.221336,
then multiplies this by 100 to give 122.1336

For using the "actual" annual rate calculation, use this formula to calculate the total with interest directly from the AER/APR, instead of the formula shown above:
"=B1*(1+E1)^(1/365)^D1"

This is the method used in the compound interest spreadsheets I have supplied.