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## Tydskrif vir Geesteswetenskappe

*On-line version* ISSN 2224-7912

#### Abstract

ROSSOUW, Jannie. **A small note about a big difference: Percentage change compared to percentage point change**.* Tydskr. geesteswet.* [online]. 2013, vol.53, n.3, pp. 481-491. ISSN 2224-7912.

Each discipline has its own terminology that often looks like an unnecessary complication for people not trained in the discipline. However, in the economic, mathematical and statistical sciences there is a major difference between percentage change and percentage point change. This note focuses on these differences. From a statistical perspective the calculation of a percentage change is quite simple, namely the difference between two values, expressed out of 100. It is calculated (for instance, when a value increases from 60 to 66) as *66-60/60 x 100/1=10%.* The accepted symbol for percentage and percentage change is "%" and originates from Italian (originally Latin), *per cento.* These calculations become more challenging when the difference between two percentages is calculated. If an examination mark increases from 60% to 66%, it is often incorrectly described as an increase of 6%, while it is an increase of 10%, namely (66/60 - 1) x 100. It is also an increase of 6 percentage points. Percentage points comprise basis points, with each percentage point comprising 100 basis points. The symbol for basis points, which has practically fallen into disuse, is ^{0}/000. The differences between percentage, percentage point, per cent change and percentage point change are of crucial importance when used incorrectly in legal documents such as contracts. A case in point is the inaccurate use of this terminology in legal documents of a South African bank. It is incorrectly stated that a promotional discount interest rate of 18,5% (calculated incorrectly in the first instance) will be increased by 3,0% when interest and capital payments are in arrears for four months or more. This implies that the penalty rate should be *[18,5/1 + 18,5/1 x 3,0/100)] = 19,055%* per annum, but it is incorrectly stated as a rate of 21,5% per annum. Although outside the scope of this note, it would be interesting to challenge this incorrect information in a court of law. The solution to the problem is to improve communication about per cent, per cent change, percentage point and percentage point change and to include training on these differences in the school curriculum. A related problem is the use of an accepted symbol for per cent and percentage change *("%"),* and its incorrect use for percentage point and percentage point change. In the latter two instances no accepted symbol has been developed, and it is concluded that the development ofsuch a symbol could go a long way towards the clarification ofdifferences described in this note. Such a symbol could, for instance, be "_{%} p" or "p %", from the symbol for per cent. An alternative could be to derive a symbol from the disused symbol for basis points (" _{%00}"), as percentage points are closer in meaning to basis points than to per cent. However, the symbol ^{o}/_{00} is not a suitable alternative, as it denotes per mille (per thousand) from Latin, although it has fallen into disuse.

**Keywords
:
**banking; basis points; economics; incorrect application of terminology; per cent; per cent change; percentage point; percentage point change; mathematics; symbol for percentage point; statistics.