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

Return the future value at the end of period

nof an investment which consists ofnpayments ofpin each period, assuming an interest rater.The optional argument

lmay be used to specify an additional lump-sum payment.The optional argument

methodmay 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

ris 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

nperiods of an initial lump sum investmentl, given a per-period interest rater.Note that the rate

ris 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

pfrom an initial investmenti(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

pnecessary to amortizealoan of amountaand interestr.The optional argument

lmay be used to specify an additional lump-sum payment oflmade at the end of the amortization time.The optional argument

methodmay 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

ris 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

pwhich occur at the ends ofnconsecutive periods.rspecifies the one-period interest rates and can either be a scalar (constant rates) or a vector of the same length asp.The optional argument

imay be used to specify an initial investment.Note that the rate

ris 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

rinnperiods.The optional argument

lmay be used to specify a terminal lump-sum payment.The optional argument

methodmay 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

pfornconsecutive periods, assuming an interestr.The optional argument

lmay be used to specify an additional lump-sum payment made at the end ofnperiods.The optional argument

methodmay 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

ris 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

pin one lump sum at the end ofnperiods, given the interest rater.Note that the rate

ris 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

vwhich payspinnconsecutive periods.The optional argument

lmay be used to specify an additional lump-sum payment made at the end ofnperiods.The optional string argument

methodmay 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 bym(e.g. the number of data per year if you want to compute the volatility per year). The optional parameterngives the number of past periods used for computation, if it is omitted, a value of 1 is used. Iftis the number of rows ofx,`vol`

returns the volatility from`n*m`

tot.