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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.

Previous: Depreciation Functions, Up: Financial Functions [Contents][Index]