**"APRs? no problem"**

Unpublished letter sent to 1 August 2002, The
Financial Times,
London**
***link*

Sir:

The Annual Percentage Rate was launched 25 years ago to provide consumers with a "true rate" benchmark. It represents an equivalent rate with interest payable annually in arrears. Thus mortgages with interest payable monthly, car loans with flat interest calculated on the initial amount and no allowance for the monthly reducing debt and deposits with simple interest only payable at the end of a five-year term have to quote the equivalent true annualised rate.

So £1 borrowed for half a year at an APR of 10% has a repayment of 1.10 raised to the power of 1/2. A cheap school calculator with a powers function produces a repayment of principal plus interest of 1.04881. Now this makes sense given that if you re-borrowed that 1.04881 at the same APR of 10% for a further six months you get 1.04881 times 1.04881 = 1.10. This is the principal of 1 plus the annual interest of 0.10 or 10%. Similarly a quarter year borrowing at the same APR has a repayment of 1.10 to the power of 1/4 which is 1.0241. Accumulating this over the year we get 1.02411 x 1.02411 x 1.02411 x 1.02411 which is indeed 1.10.

Therefore £1500 borrowed for 18 days at an APR of 14.9% in the example is repaid by £1500 times 1.149 raised to the power of 18/365 giving principal plus interest of £1510.31. No wet towels required!

Your report, comments by members of the Treasury select committee, banks' chief executives and academics do not indicate that APRs are difficult to understand. What is indeed shockingly clear is the low grasp of elementary maths in Britain. And moreover rather than expressing shame people who should know better are proud of it. No German or French banker would admit to such reported comments. And academia, rather than improving its communications skills and explaining the subject clearly is happy to go along with this sorry state of affairs by describing the sums as "so difficult to understand".

You report in ("MPs hit out at unintelligible card charges" Jul 30, 2002) that The Treasury select committee "was forced to call in a professional mathematician to calculate the interest on one bank's credit card. It took him an afternoon to do the sums." I would suggest that this is more a reflection on a poor appreciation of high school maths rather than on the complexity of the subject.

You quoted two leading banks in ("Banks say credit cards are baffling consumers", June 19, 2002), saying that "consumers would need advanced mathematics and teams of experts to work out the interest income charged on their credit card bills". You also quoted Ian Harley, chief executive of Abbey National as saying that "only with calculus could credit card interest rates be compared to choose the best card". Dr. Robert Hunt of Cambridge University's Isaac Newton Institute for Mathematical Sciences told you that "to the man in the street these things are totally impossible ... even for a professional mathematician it took some time." and Steve Round, director of the Credit Card Research Group said "It has been a bit of a nightmare".

Weighty opinions indeed! But may I
suggest that APRs are not inherently misleading. They are sometimes misused
but usually badly explained. There is certainly no need for calculus and
absolutely no need for a Cambridge doctorate let alone A level maths. All
that is required for an understanding of APRs is a grasp of powers and
roots. This is acne-level school Algebra taught a year or two before GCSEs
or "O" levels in old money. Calculus, on the other hand, is indeed
a bit more advanced, taught at first year "A" level and comes in
rather handy for valuing options and mortgage backed securities. The
confusion between Calculus and Algebra at the Abbey may perhaps explain
their poor investment results.

The Annual Percentage Rate was launched 25 years ago to provide consumers with a "true rate" benchmark. It represents an equivalent rate with interest payable annually in arrears. Thus mortgages with interest payable monthly, car loans with flat interest calculated on the initial amount and no allowance for the monthly reducing debt and deposits with simple interest only payable at the end of a five-year term have to quote the equivalent true annualised rate.

So £1 borrowed for half a year at an APR of 10% has a repayment of 1.10 raised to the power of 1/2. A cheap school calculator with a powers function produces a repayment of principal plus interest of 1.04881. Now this makes sense given that if you re-borrowed that 1.04881 at the same APR of 10% for a further six months you get 1.04881 times 1.04881 = 1.10. This is the principal of 1 plus the annual interest of 0.10 or 10%. Similarly a quarter year borrowing at the same APR has a repayment of 1.10 to the power of 1/4 which is 1.0241. Accumulating this over the year we get 1.02411 x 1.02411 x 1.02411 x 1.02411 which is indeed 1.10.

Therefore £1500 borrowed for 18 days at an APR of 14.9% in the example is repaid by £1500 times 1.149 raised to the power of 18/365 giving principal plus interest of £1510.31. No wet towels required!

Your report, comments by members of the Treasury select committee, banks' chief executives and academics do not indicate that APRs are difficult to understand. What is indeed shockingly clear is the low grasp of elementary maths in Britain. And moreover rather than expressing shame people who should know better are proud of it. No German or French banker would admit to such reported comments. And academia, rather than improving its communications skills and explaining the subject clearly is happy to go along with this sorry state of affairs by describing the sums as "so difficult to understand".

yours faithfully

warren edwardes, ceo

delphi risk management ltd

3 hyde park steps

st. george's fields

london W2 2YQ, UK

warren edwardes, ceo

delphi risk management ltd

3 hyde park steps

st. george's fields

london W2 2YQ, UK

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