(42S) 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 42S/DM42 Program: PVGROW

Both PVGROW and PVGDUE use only one register, R01.

Code:

00  {79-Byte Prgm}
01  LBL "PVGROW"
02  "BASE PMT?"
03  PROMPT
04  "INTEREST?"
05  PROMPT
06  1
07  X<>Y
08  %
09  +
10  STO 01
11  ÷
12  1
13  "GROWTH?"
14  PROMPT
15  %
16  +
17  RCL÷ 01
18  STO 01
19  "N?"
20  PROMPT
21  Y↑X
22  1
23  X<>Y
24  -
25  1
26  RCL- 01
27  ÷
28  ×
29  "PV="
30  ARCL ST X
31  AVIEW
32  END

HP 42S/DM42 Program: PVGDUE

Code:

00  {79-Byte Prgm}
01  LBL "PVGDUE"
02  "BASE PMT?"
03  PROMPT
04  "INTEREST?"
05  PROMPT
06  1
07  X<>Y
08  %
09  +
10  1
11  "GROWTH?"
12  PROMPT
13  %
14  +
15  ÷
16  1/X
17  STO 01
18  "N?"
19  PROMPT
20  1
21  +
22  Y↑X
23  1
24  X<>Y
25  -
26  1
27  RCL- 01
28  ÷
29  ×
30  "PV="
31  ARCL ST X
32  AVIEW
33  END

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