annuity.level: Level Annuity

In FinancialMath: Financial Mathematics for Actuaries

Description

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

Usage

annuity.level(pv=NA,fv=NA,n=NA,pmt=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
pmt	value of the level payments
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

Annuity Immediate:

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

fv=pmt*{s_{≤ft. {\overline {\, n \,}}\! \right |j}}=pmt*{a_{≤ft. {\overline {\, n \,}}\! \right |j}}*(1+j)^n

Annuity Due:

pv=pmt*{\ddot {a}_{≤ft. {\overline {\, n \,}}\! \right |j}}=pmt*{a_{≤ft. {\overline {\, n \,}}\! \right |j}}*(1+j)

fv=pmt*{\ddot {s}_{≤ft. {\overline {\, n \,}}\! \right |j}}=pmt*{a_{≤ft. {\overline {\, n \,}}\! \right |j}}*(1+j)^{n+1}

Value

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

Note

At least one of pv, fv, n, pmt, 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.geo

perpetuity.arith

perpetuity.geo

perpetuity.level

Examples

annuity.level(pv=NA,fv=101.85,n=10,pmt=8,i=NA,ic=1,pf=1,imm=TRUE)

annuity.level(pv=80,fv=NA,n=15,pf=2,pmt=NA,i=.01,imm=FALSE)

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