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Bank Interest

Overview

Interest is rent paid for money borrowed.  This section deals with interest on borrowings in general.  Some additional information will be found in the sections on overdrafts, loans, credit cards, mortgages

When you were at school, you probably learned about simple interest and compound interest.  You also probably did a few experiments in science.  Just as your school science did not equip you for life as a scientist, your interest calculations may not have been sufficient for real life bank borrowing. 

There is no standard way of calculating interest.  There are many variations.  7% from one institution may be different from 7% in another.  So there is legislation to create a standardised calculation for loans and mortgages called the APR (Annual Percentage Rate of Charge) which attempts to express interest and other relevant charges in a single number.

The way that interest is calculated can affect you if you want to pay off a loan ahead of schedule, or if extra interest is added if you are late in repaying.

"Penalty interest rates" can arise on overdrafts or other loans if your balance on a loan or overdraft exceeds an agreed amount.

Types of Interest Calculation

Title

How calculated

Effect annual rate if the quoted interest rate is 7%

Where typically used

Annuity with annual rests.

Interest is calculated at 1/365 of the annual rate and applied for the number of days since the most recent transaction.  The interest is accumulated separately from the balance.  The accumulated interest is added to the balance once each year.

7%

Demand deposit accounts

Annuity with annual rests - with monthly instalments on an annual repayment.

An annual instalment is calculated on the assumption that it will be paid at the end of each year.  The monthly instalment is 1/12 of this.  So monthly instalments are taken as sub-instalments of an annual instalment.  No adjustment is made to interest for the fact that 11 out of 12 instalments are paid in advance.

7.36758%

 

This calculation was popular with building societies, and is still applied by some on mortgages.

Annuity with half-yearly rests

Interest is calculated at 1/365 of the annual rate and applied for the number of days since the most recent transaction.  The interest is accumulated separately from the balance.  The accumulated interest is added to the balance twice each year.

7.12250%

 

Was the standard calculation on bank loans and overdrafts - most have moved to quarterly rests

Annuity with quarterly rests

Interest is calculated at 1/365 of the annual rate and applied for the number of days since the most recent transaction.  The interest is accumulated separately from the balance.  The accumulated interest is added to the balance four times each year.

7.18590%

 

This is the most usual method of calculating interest on bank loans and overdrafts and some mortgages

Annuity with monthly rests

Interest is calculated at 1/365 of the annual rate and applied for the number of days since the most recent transaction.  The interest is accumulated separately from the balance.  The accumulated interest is added to the balance monthly.

7.22901%

 

Frequently applied to mortgages at banks and building societies

Flat rate

Interest is calculated on the full amount lent for the entire period without reference to repayments

1-year

13.44220%

Sometimes used by finance companies etc.  Take particular care with this one as the rates are obviously misleading.  Look at the APR.

3-year

13.60963%

5-year

13.24615%

360-day calculations

Interest is calculated daily at 1/360 of the annual rate

7.09722%

Not much used in Ireland for ordinary loans, but this calculation may apply to cross-border investments and loans

How repayments are calculated

If you want to cut to the chase, you can download an Excel repayment calculator here

If you want more details read on.

You will notice above that the word "annuity" occurs in the title of most interest rate types.  A mathematical formula called the annuity formula is the core of the calculation of repayments.  Fortunately. the annuity formula is built into Excel.  Not only that, but a variety of extensions of the formula are built into Excel to make one-line calculations easy. 

The PMT function in Excel calculates a repayment per period for a situation where interest is charged (compounded) every period.  So if you have an annual interest rate, and the interest is compounded annually, and you want to calculate an annual repayment, then PMT is perfect.  If you want to calculate a monthly repayment and interest is compounded monthly, then you can use PMT, but you must divide the annual interest rate by 12

If the compounding frequency does not match the repayment frequency, then you must create a period rate.  The following is a table of how to calculate some of the most popular combinations.  The formulae for annuity-type loans are:-

Annuity-type loans

In these formulae, the following are inputs:-
"I" is the quoted annual interest rate, expressed as a decimal (e.g. 7% is expressed as .07)
"L" is the amount of the loan
"N" is the number of repayments
In these formulae, the following are results:-
"R" is the calculated repayment
"P" is the effective rate per repayment period, expressed as a decimal
"E" is the effective annual rate expressed as a decimal
Note:  In the formulae below, "^" means "to the power of"

Compounding Frequency

Monthly Quarterly Half-Yearly Annual
Repayment

Frequency

Monthly P= I/12

R= -PMT(P,N,L)

E= (1+I/12)^12-1

P= (1+I/4)^(1/3)-1

R= -PMT(P,N,L)

E= (1+I/4)^4-1

P= (1+I/2)^(1/6)-1

R= -PMT(P,N,L)

E= (1+I/2)^2-1

P= (1+I)^(1/12)-1

R= -PMT(P,N,L)

E=I

Quarterly P= (1+I/12)^3-1

R= -PMT(P,N,L)

E= (1+I/12)^12-1

P= (I/4)

R= -PMT(P,N,L)

E= (1+I/4)^4-1

P=(1+I/2)^(1/2)-1

R= -PMT(P,N,L)

E= (1+I/2)^2-1

P= (1+I)^(1/4)-1

R= -PMT(P,N,L)

E=I

Half-Yearly P= (1+I/12)^6-1

R= -PMT(P,N,L)

E= (1+I/12)^12-1

P= (1+I/2)^2-1

R= -PMT(P,N,L)

E= (1+I/2)^2-1

P= (I/2)

R= -PMT(P,N,L)

E= (1+I/2)^2-1

P= (1+I)^(1/2)-1

R= -PMT(P,N,L)

E=I

Annual P= (1+I/12)^12-1

R= -PMT(P,N,L)

E= (1+I/12)^12-1

P= (1+I/4)^4-1

R= -PMT(P,N,L)

E= (1+I/4)^4-1

E= (1+I/2)^2-1

R= -PMT(P,N,L)

E= (1+I/2)^2-1

P= I

R= -PMT(I,N,L)

E= I

For Flat Rate Loans, the formulae are:-

Flat Rate Loans

Flat Rate Loans - all repayment frequencies

R= (L+L*I*T)/N where T is the loan term in years.

P= RATE(N,R,-L)

E= (1+P^F)-1 where F is the repayment frequency expressed as number of repayments per annum.

APR (Annual Percentage Rate of Charge)

The APR is an attempt to express interest and other relevant bank charges as if they were all interest in a standardised calculation, in order to make comparison between loans easy.  The current provisions regarding APR date from the Consumer Credit Act 1995 which updates previous legislation

Among the main provisions of this legislation:-

  • A lender offering credit must show the APR rate in advertising.  If an interest rate is shown, then the APR must be shown at least as prominently.  An examination of websites and advertising of various institutions would seem to suggest that some institutions sail very close to the wind in relation to compliance with these requirements.  And at least one major bank shows on a single page here (a) 40 specific APRs for individual loan quotes (b) a statement that the "Typical APR" is 9% and (c) a statement that "Usually our rates range from 7.8% APR to 20.6% APR".  This brochure may accord with the legislation but does not help consumers much.
  • Where a precise APR cannot be shown (e.g. if it varies from customer to customer), then a representative example must be shown.  This happens for any loan product where there is a charge other than interest, and therefore normally includes overdrafts, most credit cards, and many other situations.
  • A credit agreement must be agreed between lender and borrower
  • A schedule in the credit agreement must show the APR, in addition to other information

You would never make a car purchase decision based upon the quoted miles per gallon alone.  Similarly, you should never make a decision on APR alone.  Two cars with identical miles per gallon may have very different running costs - perhaps because one car lasts twice as long as the other - in this case, the more long-lasting one will be cheaper to run.  With loans, two loans with identical APRs may have very different repayments - a longer loan will have lower repayments per month, but will have higher total repayments.

If the loans have similar characteristics - over a similar period, then the choose the one with the lowest APR.  If the loans have different characteristics, then you will have to make up your mind on whether the packages offered suit your circumstances.  Consult the appropriate leaflet available from the Financial Regulator cost surveys here

If you choose to purchase optional extras with your loan (e.g. payment protection), this will not increase the APR - but see the note below on how it will affect your loan amount.

You can be reasonably assured that the APR as quoted in advertising is accurate.  It is an offence to publish an inappropriate APR.  If, however, you want to calculate it, read on

Calculating the APR

The Consumer Credit Act 1995 describes APR in the following terms:-  "In this Act the APR shall be the equivalent, on an annual basis, of the present value of all commitments (loans, repayments and charges), future or existing, agreed by the creditor and the consumer, calculated to the nearest rounded decimal place in accordance with the method of calculation specified in the Fourth Schedule."

Annual Percentage Rate of Charge (APR) is a tricky calculation.  A free downloadable calculator called DualCalc is available from the UK office of Fair Trading here.  A comprehensive document  about the calculation (65 pages) is available from the UK Office of Fair Trading here.  Note that the UK legislation differs slightly from the Irish legislation,  but the calculation principles are the same.  Note that Bankhawk Banking Solutions accepts no responsibility in relation to the use of such calculator.

How interest is applied

Interest is frequently charged on a "per diem" basis.  Every time that a transaction arises, interest is calculated from the relevant date of the previous transaction to the relevant date of the current transaction.  The interest is accumulated up to the end of the "interest charging period" and then added to the outstanding balance of the loan.  Interest charging periods may be monthly, quarterly, half-yearly, or annual.  The relevant date as mentioned above may not always be the date on which the transaction occurred.  Where the loan is drawn down by cheque, the relevant date may be either the (a) date of issue of the cheque or (b) the date on which the cheque was paid.  In relation to repayments, the relevant date should be the date on which the lender received cleared funds.

Early Settlement

Early settlement is any circumstance whereby some or all of the loan is paid ahead of the agreed schedule.  This may arise (a) if you choose to pay a lump sum to pay off some or all of the balance or (b) if you "trade in", replacing your current loan by a larger one.  All loan agreements and mortgages contain clauses which define the calculations to be used in the event of early settlement. 

The amount to be paid off will normally be (a) the balance of the loan, including interest to the date of termination plus (b) a termination penalty, if any.  If the loan is a fixed rate loan, then the termination penalty will be significant..

Surcharges and surcharge interest

Where the amount outstanding on the loan exceeds the agreed terms of the loan, then surcharges or surcharge interest rate will likely apply.  This can happen if you borrow an amount in excess of your limit or if your repayments are late.  This may therefore arise:-

  • When an overdraft exceeds the agreed limit, Surcharge interest rates may be high or very high.  For an overdraft, the surcharge rate may be .75% per month (equivalent to over 9% per annum) in addition to the agreed overdraft rate, and is applied to the excess amount.  Some banks may also charge a fee for each item paid in excess of your limit.
  • Where a credit card balance exceeds the agreed limit.  Most credit cards carry a fee for late payment and a fee for each item paid over the limit
  • Where a loan or mortgage account is in arrears - the terms of surcharges and/or surcharge interest will be specifically laid out in the credit agreement or mortgage instrument.