Teach Secondary Issue 14.2

If you pay back your credit card balance at the end of eachmonth, then using the card will have likely not cost anything. Hold off for longer, and the credit card company will charge you interest at a pre-agreed rate – usually in the region of 20%annually. This interest will continue being added to your balance eachmonth until you pay it back. There will often be a minimumbalance that needs to be paid off – for example, ‘ 1%of the outstanding balance, or £5, whichever is greater ’. Fail to pay back enough eachmonth, and you’ll incur payment fees (usually around £12). Interest is a common application of percentages, but the information given to consumers about credit cards is often presented in ways designed to complicate how much they actually cost. Credit cards can often charge additional fees for cash withdrawals, balance transfers, overseas transactions or when you exceed your credit limit. Some may even levy an annual fee just for using the card itself. Asking students to look up howmuchmajor credit card companies charge for their fees and how often can be an illuminating experience. Mortgages This is less broadly applicable than the other examples – since those students who will eventually buy a house likely won’t do so until later in their lives – but it still involves the same mathematical ideas. Mortgage lenders charge interest on mortgages at a pre-agreed rate, and homebuyers then usually pay back their mortgages monthly until the debt is eventually cleared. Working with these kinds of calculations can help students develop an intuition for how the amount of interest you pay changes over the term of a mortgage, and howmuch difference having a large deposit canmake to the payment term and monthly costs. Some banks will offer a better interest rate if you pay a larger deposit. A project exploring this could involve looking up the cost of houses similar to the students’ own, or ones they’d like to live in, and then finding details on bank websites of what mortgage rates they offer. Given a deposit, house price bank interest rate and a monthly payment of £ x , how long will it take them to pay off their mortgage if interest is added on at the end of each year? Students could try different monthly amounts until they get a 20-year term. Howmuchmore would the monthly payment be to get a 10-year term? It can be instructive to calculate how muchmoney is paid in total over the course of a mortgage, and to investigate how a 4% interest rate and a 5% interest rate compare. Personal finance examples can serve as goodmotivation for understanding percentages, solving equations and developing an intuition for numbers. These kinds of calculations also provide good opportunities for getting students working with technology – from using spreadsheets as a mathematical tool, to figuring out how to get the most out of their calculators. Hopefully you can use these ideas to put together some activities for your own students! ABOUT THE AUTHOR Dr Katie Steckles is a mathematician, maths communicator and New Scientist columnist; she has recently worked with the BBC Bitesize team on its new set of GCSE maths revision resources, further details of which can be found via tiny.cc/ts142-LS1 PERCENTAGES IN PRACTICE The average annual percentage rate (APR) of a standard credit card is around 19%. If that’s the annual rate, how much will the interest amount to per month? If the monthly percentage increase is x %, then each month the balance will be (100 + x )% of what it was previously. After a year, the balance will be ((100 + x )%)12 times its original value. This rate can be equated to the annual rate, and solved to find a value for x . GCSE students can use trial and improvement, while A Level students can find a more precise solution using logarithms. Having established the monthly rate for a particular credit card, along with the minimum payment and late fees, we then can ask questions like: Given the interest rate and a specific balance (i.e. the cost of an item the student wants to buy), howmuch will I owe after 1, 2, 3 or 6 months if I... a) pay off the minimum amount? b) don’t pay anything at all (so that the late fee is added to the balance each month)? 19 teachwire.net/secondary M AT H S