annuity.arith: Arithmetic Annuity

In FinancialMath: Financial Mathematics for Actuaries

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

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_{≤ft. {\overline {\, n \,}}\! \right |j}}+q* \frac{{a_{≤ft. {\overline {\, n \,}}\! \right |j}}-n*(1+j)^{-n}}{j}

Annuity Due:

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

Value

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

Note

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

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

Author(s)

Kameron Penn and Jack Schmidt

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)

Example output

         Arithmetic Annuity
PV             2.338128e+03
FV             3.142248e+03
P              1.000000e+02
Q              4.000000e+00
Eff Rate       3.000000e-02
i^(2)          2.977831e-02
Periods        2.000000e+01
Years          1.000000e+01
         Arithmetic Annuity
PV             1.827106e+03
FV             3.000000e+03
P              1.000000e+02
Q              1.664438e+00
Eff Rate       5.083796e-02
i^(3)          5.000000e-02
i^(2)          5.020776e-02
Periods        2.000000e+01
Years          1.000000e+01

FinancialMath documentation built on May 1, 2019, 11:16 p.m.