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# 26. 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 ot 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.

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).

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).

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.

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).

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.

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.

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This document was generated by John W. Eaton on March, 28 2005 using texi2html