The functions in this section are basically inverses of the present value functions with respect to the various arguments.
The b M
(calc-fin-pmt) [pmt] command computes
the amount of periodic payment necessary to amortize a loan. Thus
pmt(rate,
n, amount) equals
the value of payment such that
pv(rate,
n, payment) =
amount.
The I b M
[pmtb] command does the same computation but using
pvb instead of pv. Like pv
and pvb, these functions can also take a fourth
argument which represents an initial lump-sum investment.
The H
b M key just invokes the fvl function, which
is the inverse of pvl. There is no explicit
pmtl function.
The b #
(calc-fin-nper) [nper] command computes
the number of regular payments necessary to amortize a loan. Thus
nper(rate,
payment, amount)
equals the value of n such that
pv(rate,
n, payment) =
amount. If payment is too small ever to
amortize a loan for amount at interest rate
rate, the nper function is left in
symbolic form.
The I b # [nperb]
command does the same computation but using pvb
instead of pv. You can give a fourth lump-sum
argument to these functions, but the computation will be rather
slow in the four-argument case.
The H b # [nperl]
command does the same computation using pvl. By
exchanging payment and amount you can also
get the solution for fvl. For example,
nperl(8%, 2000, 1000) = 9.006, so if you place $1000
in a bank account earning 8%, it will take nine years to grow to
$2000.
The b T
(calc-fin-rate) [rate] command computes
the rate of return on an investment. This is also an inverse of
pv: rate(n,
payment, amount)
computes the value of rate such that
pv(rate,
n, payment) =
amount. The result is expressed as a formula like
‘6.3%’.
The I b T
[rateb] and H b T [ratel]
commands solve the analogous equations with pvb or
pvl in place of pv. Also,
rate and rateb can accept an optional
fourth argument just like pv and pvb.
To redo the above example from a different perspective,
ratel(9, 2000, 1000) = 8.00597%, which says you will
need an interest rate of 8% in order to double your account in
nine years.
The b I
(calc-fin-irr) [irr] command is the
analogous function to rate but for net present
value. Its argument is a vector of payments. Thus
irr(payments) computes the
rate such that
npv(rate,
payments) = 0; this rate is known as the
internal rate of return.
The I b I
[irrb] command computes the internal rate of return
assuming payments occur at the beginning of each period.