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Full Version: (42S) Present Value of a Growing Annuity
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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.