FinancialMath (version 0.1.1)

perpetuity.arith: Arithmetic Perpetuity

Description

Solves for the present value, amount of the first payment, the payment increment amount per period, or the interest rate for an arithmetically growing perpetuity.

Usage

perpetuity.arith(pv=NA,p=NA,q=NA,i=NA,ic=1,pf=1,imm=TRUE)

Arguments

pv

present value of the annuity

p

amount of the first payment

q

payment increment amount per period

i

nominal interest rate convertible ic times per year

ic

interest conversion frequency per year

pf

the payment frequency- number of payments per year

imm

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

Value

Details

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

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

Perpetuity Immediate:

$pv=\frac{p}{j}+\frac{q}{j^2}$

Perpetuity Due:

$pv=(\frac{p}{j}+\frac{q}{j^2})*(1+j)$

See Also

perpetuity.geo

perpetuity.level

annuity.arith

annuity.geo

annuity.level

Examples

perpetuity.arith(100,p=1,q=.5,i=NA,ic=1,pf=1,imm=TRUE)

perpetuity.arith(pv=NA,p=1,q=.5,i=.07,ic=1,pf=1,imm=TRUE)

perpetuity.arith(pv=100,p=NA,q=1,i=.05,ic=.5,pf=1,imm=FALSE)