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Present value of a growing annuity
Formula
PV
value of the annuity at time=0
A
annuity payment in the first period
i
interest rate that would be compounded for each period of time
g
rate of growth of the annuity
n
number of payment periods
Formula description
An annuity is a series of equal payments or receipts that occur at evenly spaced intervals.In this case each cash flow grows by a factor of (1+g).
Calculator (
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A
i
%, percent,parts per hundred
decimal
‰, per mil,parts per thousand,per mille,permil,permille,per mill,promille
permyriad,basis point,bp,percentage in point,pip,parts per ten thousand,one-hundredth percent
parts per million,ppm
parts per billion,ppb
parts per trillion,ppt
parts per quadrillion,ppq
g
%, percent,parts per hundred
decimal
‰, per mil,parts per thousand,per mille,permil,permille,per mill,promille
permyriad,basis point,bp,percentage in point,pip,parts per ten thousand,one-hundredth percent
parts per million,ppm
parts per billion,ppb
parts per trillion,ppt
parts per quadrillion,ppq
n
PV
Precision
0
1
2
3
4
5
6
7
8
9
Formula code
C
C#
C++
Java
JavaScript
LaTeX
PHP
#include
PV = A*(1-pow(((1+g)/(1+i)),n))/(i-g)
PV = A*(1-Math.Pow(((1+g)/(1+i)),n))/(i-g)
#include
PV = A*(1-pow(((1+g)/(1+i)),n))/(i-g)
PV = A*(1-Math.pow(((1+g)/(1+i)),n))/(i-g)
PV = A*(1-Math.pow(((1+g)/(1+i)),n))/(i-g)
PV = \frac{A}{(i-g)} [1-(\frac{1+g}{1+i})^n]
$PV = $A*(1-pow(((1+$g)/(1+$i)),$n))/($i-$g)
References
Wikepedia:Present value of a growing annuity.
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