perpetuity.arith: Arithmetic Perpetuity
In FinancialMath: Financial Mathematics for Actuaries

Description Usage Arguments Details Value Note Author(s) See Also Examples

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.

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

`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)

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)

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

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

Kameron Penn and Jack Schmidt

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)