The functions in this section are basically inverses of the present value functions with respect to the various arguments.
The b M (
pmt] command computes
the amount of periodic payment necessary to amortize a loan.
pmt(rate, n, amount) equals the
value of payment such that
payment) = amount.
The I b M [
pmtb] command does the same computation
pvb instead of
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
The b # (
nper] command computes
the number of regular payments necessary to amortize a loan.
nper(rate, payment, amount) equals
the value of n such that
payment) = amount. If payment is too small
ever to amortize a loan for amount at interest rate rate,
nper function is left in symbolic form.
The I b # [
nperb] command does the same computation
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
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 (
rate] command computes
the rate of return on an investment. This is also an inverse of
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 [
commands solve the analogous equations with
in place of
accept an optional fourth argument just like
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 (
irr] command is the
analogous function to
rate but for net present value.
Its argument is a vector of payments. Thus
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.