perpetuity.geo {FinancialMath}

Geometric Perpetuity

Description

Solves for the present value, amount of the first payment, the payment growth rate, or the interest rate for a geometrically growing perpetuity.

Usage

perpetuity.geo(pv=NA,p=NA,k=NA,i=NA,ic=1,pf=1,imm=TRUE)

Arguments

pv

present value

p

amount of the first payment

k

payment growth rate per period

i

nominal interest rate convertible ic times per year

ic

interest conversion frequency per year

pf

the payment frequency- number of payments and periods per year

imm

option for perpetuity immediate or due, default is immediate (TRUE)

Details

Effective Rate of Interest: eff.i=(1+\frac{i}{ic})^{ic}-1

j=(1+eff.i)^{\frac{1}{pf}}-1

Perpetuity Immediate:

j > k: pv=\frac{p}{j-k}

Perpetuity Due:

j > k: pv=\frac{p}{j-k}*(1+j)

Value

Returns a matrix of the input variables and calculated unknown variables.

Note

One of pv, p, k, or i must be NA (unknown).

See Also

perpetuity.arith

perpetuity.level

annuity.arith

annuity.geo

annuity.level

Examples

perpetuity.geo(pv=NA,p=5,k=.03,i=.04,ic=1,pf=1,imm=TRUE)

perpetuity.geo(pv=1000,p=5,k=NA,i=.04,ic=1,pf=1,imm=FALSE)