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(71B) Present Value of a Growing Annuity - Eddie W. Shore - 01-03-2021 03:44 PM
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 ="; AExample:
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_Value_of_Growing_Annuity.html Retrieved December 13, 2020.
More information: http://edspi31415.blogspot.com/2021/01/swiss-micros-dm42-and-hp71b-present.html