## 25 Financial Functions

— Function File: fv (r, n, p, l, method)

> Return the future value at the end of period n of an investment which consists of n payments of p in each period, assuming an interest rate r.

> The optional argument l may be used to specify an additional lump-sum payment.

> The optional argument method may be used to specify whether the payments are made at the end (`"e"`, default) or at the beginning (`"b"`) of each period.

> Note that the rate r is specified as a fraction (i.e., 0.05, not 5 percent).

— Function File: fvl (r, n, l)

> Return the future value at the end of n periods of an initial lump sum investment l, given a per-period interest rate r.

> Note that the rate r is specified as a fraction (i.e., 0.05, not 5 percent).

— Function File: irr (p, i)

> Return the internal rate of return of a series of payments p from an initial investment i (i.e., the solution of `npv (r, p) = i`. If the second argument is omitted, a value of 0 is used.

> See also: npv, pv, rate.

— Function File: nper (r, p, a, l, method)

> Return the number of regular payments of p necessary to amortize a loan of amount a and interest r.

> The optional argument l may be used to specify an additional lump-sum payment of l made at the end of the amortization time.

> The optional argument method may be used to specify whether payments are made at the end ("e", default) or at the beginning ("b") of each period.

> Note that the rate r is specified as a fraction (i.e., 0.05, not 5 percent).

> See also: pv, pmt, rate, npv.

— Function File: npv (r, p, i)

> Returns the net present value of a series of irregular (i.e., not necessarily identical) payments p which occur at the ends of n consecutive periods. r specifies the one-period interest rates and can either be a scalar (constant rates) or a vector of the same length as p.

> The optional argument i may be used to specify an initial investment.

> Note that the rate r is specified as a fraction (i.e., 0.05, not 5 percent).

> See also: irr, pv.

— Function File: pmt (r, n, a, l, method)

> Return the amount of periodic payment necessary to amortize a loan of amount a with interest rate r in n periods.

> The optional argument l may be used to specify a terminal lump-sum payment.

> The optional argument method may be used to specify whether payments are made at the end ("e", default) or at the beginning ("b") of each period.

> See also: pv, nper, rate.

— Function File: pv (r, n, p, l, method)

> Returns the present value of an investment that will pay off p for n consecutive periods, assuming an interest r.

> The optional argument l may be used to specify an additional lump-sum payment made at the end of n periods.

> The optional argument method may be used to specify whether payments are made at the end (`"e"`, default) or at the beginning (`"b"`) of each period.

> Note that the rate r is specified as a fraction (i.e., 0.05, not 5 percent).

> See also: pmt, nper, rate, npv.

— Function File: pvl (r, n, p)

> Return the present value of an investment that will pay off p in one lump sum at the end of n periods, given the interest rate r.

> Note that the rate r is specified as a fraction (i.e., 0.05, not 5 percent).

— Function File: rate (n, p, v, l, method)

> Return the rate of return on an investment of present value v which pays p in n consecutive periods.

> The optional argument l may be used to specify an additional lump-sum payment made at the end of n periods.

> The optional string argument method may be used to specify whether payments are made at the end (`"e"`, default) or at the beginning (`"b"`) of each period.

> See also: pv, pmt, nper, npv.

— Function File: vol (x, m, n)

> Return the volatility of each column of the input matrix x. The number of data sets per period is given by m (e.g. the number of data per year if you want to compute the volatility per year). The optional parameter n gives the number of past periods used for computation, if it is omitted, a value of 1 is used. If t is the number of rows of x, `vol` returns the volatility from `n*m` to t.