FinancialMath (version 0.1.1)

annuity.arith: Arithmetic Annuity

Description

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

Usage

annuity.arith(pv=NA,fv=NA,n=NA,p=NA,q=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

p

amount of the first payment

q

payment increment amount per period

i

nominal interest frequency 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)

plot

option to display a time diagram of the payments

Value

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:

$pv=p*{a_{\left. {\overline {\, n \,}}\! \right |j}}+q* \frac{{a_{\left. {\overline {\, n \,}}\! \right |j}}-n*(1+j)^{-n}}{j}$

Annuity Due:

$pv=(p*{a_{\left. {\overline {\, n \,}}\! \right |j}}+q* \frac{{a_{\left. {\overline {\, n \,}}\! \right |j}}-n*(1+j)^{-n}}{j})*(1+i)$

See Also

annuity.geo

annuity.level

perpetuity.arith

perpetuity.geo

perpetuity.level

Examples

annuity.arith(pv=NA,fv=NA,n=20,p=100,q=4,i=.03,ic=1,pf=2,imm=TRUE)

annuity.arith(pv=NA,fv=3000,n=20,p=100,q=NA,i=.05,ic=3,pf=2,imm=FALSE)