Arithmetic Perpetuity
Solves for the present value, amount of the first payment, the payment increment amount per period, or the interest rate for an arithmetically growing perpetuity.
perpetuity.arith(pv=NA,p=NA,q=NA,i=NA,ic=1,pf=1,imm=TRUE)
pv |
present value of the annuity |
p |
amount of the first payment |
q |
payment increment amount per period |
i |
nominal interest rate 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) |
Effective Rate of Interest: eff.i=(1+\frac{i}{ic})^{ic}-1
j=(1+eff.i)^{\frac{1}{pf}}-1
Perpetuity Immediate:
pv=\frac{p}{j}+\frac{q}{j^2}
Perpetuity Due:
pv=(\frac{p}{j}+\frac{q}{j^2})*(1+j)
Returns a matrix of input variables, and calculated unknown variables.
One of pv, p, q, or i must be NA (unknown).
Kameron Penn and Jack Schmidt
perpetuity.arith(100,p=1,q=.5,i=NA,ic=1,pf=1,imm=TRUE) perpetuity.arith(pv=NA,p=1,q=.5,i=.07,ic=1,pf=1,imm=TRUE) perpetuity.arith(pv=100,p=NA,q=1,i=.05,ic=.5,pf=1,imm=FALSE)
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