# Interest Tutorial

## INTEREST TUTORIAL

With thanks to Steven4064

The calculation of interest seems to be a subject that causes a deal of confusion. The purpose of this tutorial is to explain the concepts and help to give people an understanding of what they are charged and why, and what the can claim back as part of a claim for bank and other charges.

Firstly, some definitions

Principal

On a fixed sum loan, this is the amount borrowed.

Fixed-Sum Credit

A loan where the sum borrowed (the Principal) is fixed and repaid at interest over a fixed period. Bank loans are the prime example of Fixed-sum Credit.

Running Account Credit

A loan where the sum borrowed can be continuously varied. Repayments are subject to a minimum repayment but there is no fixed term. Credit Cards and bank overdrafts are the prime examples of Running Account Credit.

Balance (Account Balance)

The amount owing at a particular time.

Period Interest rate

The effective interest rate (what you actually pay) for the period in question – usually one month.

Effective Daily Rate (EDR)

The Period Interest Rate when the period is one day. It is usually calculated from the monthly or annual rate.

Nominal Annual Rate (NAR)

If the period is one month the NAR = 12* monthly rate.

For a daily rate, NAR = 365 * EDR.

The Nominal Annual Rate is what you would be charged if you were being charged simple interest. This never happens. What you actually pay is the Effective Annual Rate.

Effective Annual Rate (EAR)

The Effective Annual Rate is the annual rate you actually pay. It is the period rate compounded over one year (see compound interest).

Annual Percentage Rate (APR)

This is the Effective Annual Rate rounded to one decimal place. The rate specified and defined by the OFT to allow different loan terms to be compared.

How APR is to be calculated is specified in the OFT booklet “Credit Charges and APR” (OFT144).

Interest date

The date on which interest is added to the account. This is usually at the end of each month.

Total Cost of Credit

For a fixed-sum loan this is the amount the borrower pays the loan company for the privilege of borrowing the money. It is calculated as the sum of all the repayments minus the principal.

Simple interest

Interest that is calculated on the outstanding balance of the principal alone. Interest is not charged on any interest previously charged.

Compound Interest

Interest that is calculated on the account balance. This balance includes the outstanding balance of the principal plus any interest previously charged.

Contractual Interest

Contractual Interest is the interest rate you are charged in a contract (eg the EAR on a credit card). The term is used in at least two different ways on this site:

• The interest levied by the bank on the account balance, on unlawful bank charges and PPI payments, etc

• Interest claimed at the bank’s normal rate in restitution for their ‘unjust enrichment’

The term 'contractuial interest' is not a term used generally. If you are claiming interest in restitution, you should use the term 'compound interest'.

Restitution

This is a legal term that means putting things back as they were (or would have been) if a certain event had not occurred (for example being mis-sold PPI). In the case of unlawful charges or mis-sold insurance, there are two 'wrongs'. Firstly, the bank or financial institution uses the money they have wrongly obtained to make a profit. This is unjust enrichment or unlawful profit. Restitution would mean that they had to give up that profit, which is just compound interest they charged on the amount wrongly obtained. Secondly, the person wronged would be deprived of the money and, in principle, would have to borrow money at commercial rates of compound interest to replace it. Again, the loss (or damages) to the wronged person is just the compound interest on the amount wrongly taken.

These are described in more detail later.

## Simple Interest

Simple interest is calculated by applying the period rate to the principal (or outstanding balance of the principal) alone. No interest is added to interest previously charged. For example, for a principal of £100 and monthly rate of 2% (note: 2% = 0.02):

At the end of the first month the balance (assuming no payments) would be

£100 + (£100 * 0.02) = £102

At the end of the second month the balance would be

£100 + (£100 * 0.02) + (£100 * 0.02) = £104

and so on. The interest over one year would be

£100 * (0.02) * 12 = £24

The Effective Annual Rate is therefore 24%.

The only time you will come across simple interest is in claiming interest under section 69 of the County Courts Act 1984. This allows the Claimant to claim simple interest on the claim at 8% per annum (0.022%/day) from the date of each charge to the date of judgement or earlier settlement.

## Compound Interest

Compound interest is calculated by applying the period rate to the total outstanding balance (balance of the principal plus interest already applied). For example, consider a principal of £100 and monthly rate of 2% (note: 2% = 0.02):

At the end of the first month the balance (assuming no payments) would be

£100 + £100 * 0.02 = £100 * (1 + 0.02) = £102

At the end of the second month the balance would be

£102 + 0.02 * £102 = £102 * (1 + 0.02) = £104.04

This can also be written as

£100 * (1 + 0.02) * (1 + 0.02) = £104.04

For 12 months we have

£100 * (1 + 0.02) * (1 + 0.02) * …… (12 times), which we write as

£100 * (1 + 0.02)^12

On this basis, the balance at the end of 1 year would be

£100 * (1 + 0.02)^12 = £126.82

and the total interest is £26.82, an Effective Annual Rate of 26.82% or an APR of 26.8%.

This is the way that all banks, credit card companies and loan companies calculate interest. The only difference is that banks, etc do the calculation daily rather than monthly.

## Total Cost of Credit and APR

The above definitions and examples ignore the effects of making repayments. Assuming a loan with monthly payments, the balance at the end of the first month would actually be

balance 1 = principal * (1 + monthly rate) – payment 1

and, at the end of the second month

balance 2 = balance 1 * (1 + monthly rate) – payment 2

and so on.

Under the Consumer Credit Act 1974 your loan must contain certain information – amount borrowed (principal), monthly payments, number of payments and APR.

The monthly repayments are calculated so that at the end of the loan period of n months (2 years - n=24; 3 years - n=36, and so on)

balance n = 0.

Most loans will also have the Credit Charge or Total Cost of Credit listed or the Total Payable.

The Total Payable is just the total of all the monthly payments plus any special initial or final payments. Typically a loan over n months will have an initial payment (which may or may not be the same as the regular monthly payment), a final payment and n-2 regular monthly payments. So

Total Payable = initial payment + (n-2) * regular payment + final payment

And the Total Cost of Credit or Credit Charge will be

Total Cost of Credit = Total payable – Principal

Calculating the APR from the Principal and Total Cost of Credit or monthly payment information is very complex. The OFT used to provide a free piece of software for doing it called DualCalc but no longer support it. However, you can download it here.

One implication of all this is that, early in the loan period, most of the repayments are going to pay off interest rather than principal. This is why early repayment ‘deals’ often require payments rather more than the original principal even though a significant amount has been paid.

For Running Account Credit (eg credit cards), it is not possible to give a figure for the Total Cost of Credit as neither the loan amount nor the repayments are fixed. However, the APR has to be given on the Credit Card Agreement along with the credit limit (or how it will be determined) and the minimum monthly payments (or how they will be calculated).

## Claiming Interest

What interest can I claim?

If you are claiming unlawful charges from a bank, credit card company or finance company or claiming back PPI payments, you can claim back the interest they have levied on the charges you are reclaiming.

You can also claim interest specified under s69 of the County Courts Act 1984 calculated as simple interest at 8% per annum (0.022%/day) on all the charges and interest levied on those charges from the date of the charge until the date of (court) judgement or earlier settlement. You can only claim this interest when you file a claim in court.

Instead of s69 interest, some people are claiming interest in restitution for the ‘unjust enrichment’ of the bank, credit card company or finance company. The argument is that the bank has used my money to lend to other people at interest and therefore made a profit for the bank. In order to put things back as they would have been had the bank not used my money in this way (restitution), that profit ought to be taken off them. This profit is calculated as compound interest at the bank’s normal interest rate on all the charges and interest levied on those charges from the date of the charge until the date of (court) judgement or earlier settlement. Interest for restitution is supported by case law (Sempra Metals) - you can read a summary of the case in the [Times]

What interest can I not claim?

You cannot claim overdraft interest on ‘legitimate’ overdrafts, that is, on that portion of overdrafts not made up of unlawful charges. Similarly you cannot claim back interest on purchases made with a credit card, nor the interest charged on a fixed-sum loan.

## Estimating interest charged

You can claim back the interest you have had levied on the charges you are reclaiming. The problem is that you can only calculate this exactly if you have access to every transaction on your account and to the software the bank use to calculate the interest. Obviously, we get all the transactions from the bank or credit card statements sent in response to a Subject Access Request. However, there is no way of obtaining exact information on how the bank calculates interest charges. Therefore, we need a method of estimating this interest.

PPI on loan agreements

This is actually the easiest to calculate. On a properly executed agreement you will find the following information: • PPI charges • APR Calculate the number of years since the agreement came into force. This can be years and parts of year expressed as a decimal (eg 2 years and 145 days is 2+(145/365) = 2.397 years) – call this ‘y’, say.

Interest on the PPI is then

PPI * (1 + APR)^y – PPI

(Remember to express the APR as a decimal – 26% should go in the equation as 0.26)

Current Accounts

Most banks use a complicated method of charging overdraft interest based on a daily rate applied to the daily balance with the interest charge added up and charged at the end of the month. There is no interest charge if the account is in credit or if the balance is above any agreed free overdraft limit.

The simplest way of estimating the interest on charges is to keep a running total of charges and then multiply each interest charge on the statement by the proportion of the balance attributable to charges at the interest date:

Interest on charges = Total charges to date/Account balance * interest charge.

Having done this for each interest charge on the statements, add them up to get the total interest charged on the bank charges being reclaimed. This method is the one used in the Advanced Spreadsheets in the Bank Templates Library. Remember that an overdraft balance is negative.

Credit Cards

The method used by credit card companies to add interest is very similar to the method used by banks for calculating the interest on overdrafts. The same Advanced Spreadsheet can be used as for Current Account charges. Alternatively, you can use this simpler spreadsheet. Again, remember that the credit card balance is negative.

Check

Some people are very surprised when they first calculate the interest on charges for their claim as it seems too big. This is because compound interest mounts up very quickly. As a simple ‘sanity check’ you can apply the following:

At 14% APR a debt doubles roughly every 5 years

At 19% APR a debt doubles roughly every 4 years

At 26% APR a debt doubles roughly every 3 years

At 32% APR a debt doubles roughly every 30 months

At 40% APR a debt doubles roughly every 2 years

See the original thread here for a tutorial on how to calclate interest using the Advanced Spreadsheets