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Mathagony Aunt

Q) I was teaching a top set Year 11 about compound interest and one of them asked me the difference between AER and APR. I said I would show them next week. I don't like to ask my colleagues as I feel it is something I really should know.

A) APR stands for the annual percentage rate - the rate you pay for money you borrow; AER stands for annual equivalent rate - paid to you on money that you have invested.

The APR is the rate of interest (which includes not only the interest payment but also all the lender's fees) charged on a loan on an annual basis. The APR is, if you like, the cost of a loan. The lender is legally obliged to quote the APR as this is a reflection of the true cost of borrowing. However, the interest rate on a loan can differ from the APR quite remarkably, as the APR takes into account the principal and the total money paid over the year, together with the term of the loan.

The AER is a rate that is usually quoted for interest on current, deposit or savings accounts and investments. This rate illustrates the amount of return in interest that you would expect if the interest was compounded and paid annually instead of monthly or some other regular period.

For UK taxpayers, 20 per cent of any interest earnings calculation is deducted as a taxable source of income.

This important topic would form a good set of lessons that will help pupils understand percentages more fully and provide life skills. Give an introduction on the difference between APR and AER. Focusing on credit cards would be a good start. Ask the class to collect as many leaflets as they can about different credit card offers. They could also get this information on the internet. Typing "0% credit cards" into a search engine brings up lots of different cards.

Arrange the class into groups of four and ask them to analyse the deals on a selection of credit cards. The idea is to get the whole class to consider as many different sources of information as possible, so groups will be looking at different cards from other groups. Store cards and general credit cards could be put into separate lists.

In their groups, they are to record the APR and summarise any introductory rates, interest-free periods, rebates when switching cards, loyalty and reward schemes, and waived annual fees associated with that card.

Summarise these as a whole class and discuss how you would decide is the "best deal" and why. If you have summarised this on an interactive whiteboard, it can be saved and used as information for the next lesson; otherwise you could use a flip chart or large piece of paper.

Working in groups of four for the second and third lesson, each group is given a summary information sheet related to the cards (or reminded of the information on the flip chart) and three different credit cards, which can be store cards or general credit cards.

Pupils are told that they have built up a card debt of pound;1,500 in total on three different cards and they are now going to look at managing that debt using the different cards for a two-year period (there could also be the possibility of taking out a two-year loan, but pupils might suggest this and then do the research on the web to see if this is a better option). They are told that they manage to pay back only the minimum payment required by the loan company each month, normally about 2.25 per cent to 5 per cent of the amount owing. The most successful group will be the one with the smallest amount owing at the end of the investigation.

Each group gives a presentation to the class about the decisions they have made so they need to make notes as they progress. This could be filmed for the school website.

For the able student there is a very full explanation of the equations used in the calculation process related to AER at the British Bankers Association website and Q) How do you work out hat size?

A) To work out your hat size, you measure around your head just above the brow and just above your ears. Measure this in inches and divide the result by pi, rounding the answer to the nearest eighth of an inch as this is the UK scale for hat sizes, with the smallest generally being 612 and the largest being 8. American sizes are an eighth of an inch larger than UK sizes but also use the Imperial measure.

The European measure is in centimetres and is the measure of the circumference of the head, this varies from 52-64cm.

Email your questions to Mathagony Aunt at Or write to TES Teacher, Admiral House, 66-68 East Smithfield, London E1W 1BX

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