Geometric Perpetuity
Solves for the present value, amount of the first payment, the payment growth rate, or the interest rate for a geometrically growing perpetuity.
perpetuity.geo(pv=NA,p=NA,k=NA,i=NA,ic=1,pf=1,imm=TRUE)
pv |
present value |
p |
amount of the first payment |
k |
payment growth rate per period |
i |
nominal interest rate convertible ic times per year |
ic |
interest conversion frequency per year |
pf |
the payment frequency- number of payments and periods per year |
imm |
option for perpetuity immediate or 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:
j > k: pv=\frac{p}{j-k}
Perpetuity Due:
j > k: pv=\frac{p}{j-k}*(1+j)
Returns a matrix of the input variables and calculated unknown variables.
One of pv, p, k, or i must be NA (unknown).
perpetuity.geo(pv=NA,p=5,k=.03,i=.04,ic=1,pf=1,imm=TRUE) perpetuity.geo(pv=1000,p=5,k=NA,i=.04,ic=1,pf=1,imm=FALSE)
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