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percentage
Way of representing a number as a fraction of 100. For example, 45 percent (45%)
equals 45/100, and 45% of 20 is 45/100 × 20 = 9.
Percentage increase/decrease
In general, if a quantity changes from one value to another then
percentage = 100 × (difference in the values)/old value
For example, in a sale the price of a bicycle is reduced from £120 to £90, that is there is
a discount of £30. The percentage decrease is 100 × 30/120 = 25%.
Fractions as percentages
To express a fraction as a percentage, its denominator must first be converted to 100.
For example, value-added tax (VAT) as a fraction is 7/40:
7/40 = 17.5/100 = 17.5%
The use of percentages often makes it easier to compare fractions that do not have a
common denominator (a number divisible by both the bottom numbers), for instance
when comparing rates of inflation or rates of simple interest.
To convert a fraction to a percentage on a calculator, divide the numerator by the
denominator and then multiply by 100. The percentage will correspond to the first two
figures of the decimal; for example, 7/12 = 0.5833333 = 58.3% (correct to 1 decimal
place), and 7/32 = 0.21875 = 21.9% (correct to 1 decimal place).
The percentage sign is thought to have been derived as an economy measure when
recording in old counting houses; writing in the numeric symbol for 25/100 would take
two lines of parchment, and hence the ‘100’ denominator was put alongside the 25 and
rearranged to ‘%’.
interest
In finance, a sum of money paid by a borrower to a lender in return for the loan, usually
expressed as a percentage per annum. Simple interest is interest calculated as a straight
percentage of the amount loaned or invested. In compound interest, the interest earned
over a period of time (for example, per annum) is added to the investment, so that at the
end of the next period interest is paid on that total.
'Compound interest' means that it accounts for interest earned on interest if you do not
take money out. This is the way all savings accounts work.
compound interest
Interest calculated by computing the rate against the original capital plus reinvested
interest each time the interest becomes due. When simple interest is calculated, only the
interest on the original capital is added.
For example, 10% compound interest on £2,000 over three years can be calculated as
follows:
2,000 × 1.13 = 2,662
where the multiplier is arrived at by 1 ± the percentage as a decimal, with the power
being the number of years over which the interest is to be calculated.