(71B) Present Value of a Growing Annuity

[Eddie W. Shore]

Introduction

Today we are going to calculate the present value of a growing annuity. Unlike most annuities where the payment is constant, in a growing annuity, the payment increases each period. For this particular blog, we are working with annuities that payments increase by a growth percent (g%) each period. The annuity has an different interest rate (r%) in which payments are discounted.

Variables:

P = base payment (the first payment)
g = growth rate per period
r = interest rate per period
n = number of periods
PV = present value

Present Value of a Growing Annuity - Ordinary

PV = P/(1+r) * (1 - w^n)/(1 - w)

Present Value of a Growing Annuity - Due

PV = P * (1 - w^(n+1))/(1 - w)

HP 71B Program: PVGROW

Note: This is for both ordinary and growing annuities due.

Code:

100  DESTROY P,G,R,W,A,C
105  INPUT "PAYMENT? "; P
110  INPUT "INTEREST? "; R
115  R=.01*R
120  INPUT "GROWTH? "; G
125  G=.01*G
130  W=(1+G)/(1+R)
135  INPUT "N? "; N
140  INPUT "DUE?(Y=1,N=0) ";C
145  IF C=1 THEN 200
150  IF C=0 THEN 300 ELSE 140 

200  A=P*(1-W^(N+1))/(1-W) @ ! DUE
205  GOTO 400

300  A=P*(1-W^N)/((1+R)*(1-W)) @ ! ORD
305 GOTO 400

400 PRINT "PV ="; A

Example:

Base Payment: P = 20.00
Interest Rate: r = 4%
Growth Rate: g = 5%
n = 5

Ordinary Growing Annuity

Result: PV = 98.02

Growing Annuity Due

Result: PV = 122.92

Source:

"Present Value of a Growing Annuity" financeformulas.net https://financeformulas.net/Present_Valu...nuity.html Retrieved December 13, 2020.


More information: http://edspi31415.blogspot.com/2021/01/s...esent.html