AER and APR
Annual percentage rate (APR)
Annual percentage rate is a figure which does not only give the interest rate but also takes into account any charges and costs of the borrowing.
APR is a figure given for all mortgages, loans and credit cards and there is an exact method the bank uses to calculate the figure as specified by the Financial Service Authority. The representative APR is a figure that is easily compared between different accounts. The calculation for APR takes into account all the fees and costs you must pay on top of the basic interest rate.
Representative APR
When accounts are advertised, the APR figure they will use will be the representative APR. It does not mean everyone definitely gets this rate. They will need to do credit checks for each individual and then decide who is eligible for this rate of interest. The current EU rules state that at least 51% of people who apply must get the advertised rate. This means 49% of people could actually be charged a higher rate than what is advertised.
Personal APR
The personal APR is the rate you actually pay once you have applied for the loan and the credit company has assessed your suitability. This could be very different to the representative APR and it is important you check the rate you are being offered.
For a mortgage, the representative APR and personal APR are the same.
Question
Gareth has applied for a loan of £10,000 which has a representative APR of 6%. On application to the company, the personal APR he is offered is 8.2%. How much more does the personal APR cost in comparison to the representative APR?
Representative APR
6% of £10,000.
= \(\frac{6}{100}\) x 10,000.
= £600.
£10,000 + £600 = £10,600.
The amount he repays is £10,600.
Personal APR
8.2% of £10,000.
= \(\frac{8.2}{100}\) x 10,000.
= £820.
£10,000 + £820 = £10,820.
The amount he repays is £10,820.
Therefore, the difference between the two rates is:
£10,820 – £10,600 = £220.
You can also use this method where you start by finding the difference between the two interest rates:
8.2% - 6% = 2.2%
2.2% of 10,000 = \(\frac{2.2}{100}\) x 10,000
= £220
Annual equivalent rate (AER)
An annual equivalent rate (AER) is used in the UK as an overall rate to make comparisons between saving accounts only. It is similar to compound interestThis arises when interest on an investment is calculated and added and then this interest payment also earns interest. in that the first time interest is calculated, the value of the interest is combined with the original amount. When the interest is calculated again, the new amount is used.
You will have interest on your interest which makes you more money. The interest can be compounded quite a number of times in one year depending on how often the bank calculates the interests during the year.
This is the formula to calculate AER:
\({AER}~=~({1}~+~\frac {i} {n}){^n}~-~{1}\)
i is the interest rate as a decimal
n is the number of times the interest is paid throughout one year.
This formula is given in the formula list of your exam.
Question
A savings account has quoted an interest rate of 8% that pays interest on a monthly basis. Calculate the AER of this account.
\({AER}~=~({1}~+~\frac {i} {n}){^n}~-~{1}\)
\({AER}~=~({1}~+~\frac {0.08} {12})^{12}~-~{1}\)
\({AER}~=~{0.08299950681}\)
To convert to a percentage, multiply by 100.
\({AER}~=~{8.299950681}\percent\)
\({AER}~=~{8.30}\percent\) to two decimal places.
