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.
HP 42S/DM42 Program: PVGDUE
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
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 ENDHP 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 ENDExample:
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