(42S) Present Value of a Growing Annuity - Printable Version +- HP Forums (https://www.hpmuseum.org/forum) +-- Forum: HP Software Libraries (/forum-10.html) +--- Forum: General Software Library (/forum-13.html) +--- Thread: (42S) Present Value of a Growing Annuity (/thread-16116.html) (42S) Present Value of a Growing Annuity - Eddie W. Shore - 01-03-2021 03:51 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 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_Value_of_Growing_Annuity.html Retrieved December 13, 2020. More information: http://edspi31415.blogspot.com/2021/01/swiss-micros-dm42-and-hp71b-present.html