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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.
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