calc: Percentages
8.6.1 Percentages
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The ‘M-%’ (‘calc-percent’) command takes a percentage value, say 5.4,
and converts it to an equivalent actual number. For example, ‘5.4 M-%’
enters 0.054 on the stack. (That’s the <META> or <ESC> key combined
with ‘%’.)
Actually, ‘M-%’ creates a formula of the form ‘5.4%’. You can enter
‘5.4%’ yourself during algebraic entry. The ‘%’ operator simply means,
“the preceding value divided by 100.” The ‘%’ operator has very high
precedence, so that ‘1+8%’ is interpreted as ‘1+(8%)’, not as ‘(1+8)%’.
(The ‘%’ operator is just a postfix notation for the ‘percent’ function,
just like ‘20!’ is the notation for ‘fact(20)’, or twenty-factorial.)
The formula ‘5.4%’ would normally evaluate immediately to 0.054, but
the ‘M-%’ command suppresses evaluation as it puts the formula onto the
stack. However, the next Calc command that uses the formula ‘5.4%’ will
evaluate it as its first step. The net effect is that you get to look
at ‘5.4%’ on the stack, but Calc commands see it as ‘0.054’, which is
what they expect.
In particular, ‘5.4%’ and ‘0.054’ are suitable values for the RATE
arguments of the various financial functions, but the number ‘5.4’ is
probably _not_ suitable—it represents a rate of 540 percent!
The key sequence ‘M-% *’ effectively means “percent-of.” For example,
‘68 <RET> 25 M-% *’ computes 17, which is 25% of 68 (and also 68% of 25,
which comes out to the same thing).
The ‘c %’ (‘calc-convert-percent’) command converts the value on the
top of the stack from numeric to percentage form. For example, if 0.08
is on the stack, ‘c %’ converts it to ‘8%’. The quantity is the same,
it’s just represented differently. (Contrast this with ‘M-%’, which
would convert this number to ‘0.08%’.) The ‘=’ key is a convenient way
to convert a formula like ‘8%’ back to numeric form, 0.08.
To compute what percentage one quantity is of another quantity, use
‘/ c %’. For example, ‘17 <RET> 68 / c %’ displays ‘25%’.
The ‘b %’ (‘calc-percent-change’) [‘relch’] command calculates the
percentage change from one number to another. For example, ‘40 <RET> 50
b %’ produces the answer ‘25%’, since 50 is 25% larger than 40. A
negative result represents a decrease: ‘50 <RET> 40 b %’ produces
‘-20%’, since 40 is 20% smaller than 50. (The answers are different in
magnitude because, in the first case, we’re increasing by 25% of 40, but
in the second case, we’re decreasing by 20% of 50.) The effect of ‘40
<RET> 50 b %’ is to compute ‘(50-40)/40’, converting the answer to
percentage form as if by ‘c %’.
Info Catalog
calc: Financial Functions
calc: Financial Functions
calc: Future Value