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GNU Emacs Calc 2.02 Manual

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### 8.6.4 Related Financial Functions

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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