For your reference, here are the actual formulas used to compute Calc’s financial functions.
Calc will not evaluate a financial function unless the rate or
n argument is known. However, payment or amount can
be a variable. Calc expands these functions according to the
formulas below for symbolic arguments only when you use the a "
(calc-expand-formula) command, or when taking derivatives or
integrals or solving equations involving the functions.
These formulas are shown using the conventions of Big display
mode (d B); for example, the formula for fv written
linearly is ‘pmt * ((1 + rate)^n) - 1) / rate’.
n
(1 + rate) - 1
fv(rate, n, pmt) = pmt * ---------------
rate
n
((1 + rate) - 1) (1 + rate)
fvb(rate, n, pmt) = pmt * ----------------------------
rate
n
fvl(rate, n, pmt) = pmt * (1 + rate)
-n
1 - (1 + rate)
pv(rate, n, pmt) = pmt * ----------------
rate
-n
(1 - (1 + rate) ) (1 + rate)
pvb(rate, n, pmt) = pmt * -----------------------------
rate
-n
pvl(rate, n, pmt) = pmt * (1 + rate)
-1 -2 -3
npv(rate, [a, b, c]) = a*(1 + rate) + b*(1 + rate) + c*(1 + rate)
-1 -2
npvb(rate, [a, b, c]) = a + b*(1 + rate) + c*(1 + rate)
-n
(amt - x * (1 + rate) ) * rate
pmt(rate, n, amt, x) = -------------------------------
-n
1 - (1 + rate)
-n
(amt - x * (1 + rate) ) * rate
pmtb(rate, n, amt, x) = -------------------------------
-n
(1 - (1 + rate) ) (1 + rate)
amt * rate
nper(rate, pmt, amt) = - log(1 - ------------, 1 + rate)
pmt
amt * rate
nperb(rate, pmt, amt) = - log(1 - ---------------, 1 + rate)
pmt * (1 + rate)
amt
nperl(rate, pmt, amt) = - log(---, 1 + rate)
pmt
1/n
pmt
ratel(n, pmt, amt) = ------ - 1
1/n
amt
cost - salv
sln(cost, salv, life) = -----------
life
(cost - salv) * (life - per + 1)
syd(cost, salv, life, per) = --------------------------------
life * (life + 1) / 2
book * 2
ddb(cost, salv, life, per) = --------, book = cost - depreciation so far
life
In pmt and pmtb, ‘x=0’ if omitted.
These functions accept any numeric objects, including error forms, intervals, and even (though not very usefully) complex numbers. The above formulas specify exactly the behavior of these functions with all sorts of inputs.
Note that if the first argument to the log in nper is
negative, nper leaves itself in symbolic form rather than
returning a (financially meaningless) complex number.
‘rate(num, pmt, amt)’ solves the equation
‘pv(rate, num, pmt) = amt’ for ‘rate’ using H a R
(calc-find-root), with the interval ‘[.01% .. 100%]’
for an initial guess. The rateb function is the same except
that it uses pvb. Note that ratel can be solved
directly; its formula is shown in the above list.
Similarly, ‘irr(pmts)’ solves the equation ‘npv(rate, pmts) = 0’ for ‘rate’.
If you give a fourth argument to nper or nperb, Calc
will also use H a R to solve the equation using an initial
guess interval of ‘[0 .. 100]’.
A fourth argument to fv simply sums the two components
calculated from the above formulas for fv and fvl.
The same is true of fvb, pv, and pvb.
The ddb function is computed iteratively; the “book” value
starts out equal to cost, and decreases according to the above
formula for the specified number of periods. If the book value
would decrease below salvage, it only decreases to salvage
and the depreciation is zero for all subsequent periods. The ddb
function returns the amount the book value decreased in the specified
period.