annuity.geo {FinancialMath}

Geometric Annuity

Description

Solves for the present value, future value, number of payments/periods, amount of the first payment, the payment growth rate, and/or the interest rate for a geometrically growing annuity. It can also plot a time diagram of the payments.

Usage

annuity.geo(pv=NA,fv=NA,n=NA,p=NA,k=NA,i=NA,ic=1,pf=1,imm=TRUE,plot=FALSE)

Arguments

pv

present value of the annuity

fv

future value of the annuity

n

number of payments/periods for the annuity

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/periods per year

imm

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

plot

option to display a time diagram of the payments

Details

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

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

fv=pv*(1+j)^n

Annuity Immediate:

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

j = k: pv=p*\frac{n}{1+j}

Annuity Due:

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

j = k: pv=p*n

Value

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

Note

At least one of pv, fv, n, pmt, k, or i must be NA (unknown).

pv and fv cannot both be specified, at least one must be NA (unknown).

See Also

annuity.arith

annuity.level

perpetuity.arith

perpetuity.geo

perpetuity.level

Examples

annuity.geo(pv=NA,fv=100,n=10,p=9,k=.02,i=NA,ic=2,pf=.5,plot=TRUE)

annuity.geo(pv=NA,fv=128,n=5,p=NA,k=.04,i=.03,pf=2)