| annuity.arith {FinancialMath} | R Documentation |
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 |
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)
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
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)