(17B/19B) GPM: initial payment

[Werner]

(05-27-2024 11:29 AM)SlideRule Wrote:  Professional Real Estate Problem Solving Using the HP 12C {2e}, © 1993, 1997

In this (excellent) book, the initial payment in a Gradual Payment Mortgage is determined using the Cash Flows functionality of the 12C. There is another way, using the basic TVM functionality:

[f] [CLEAR FIN]
[g] [END]

NP [N]
I% [i]
[STO] [PMT]
G% [CHS] [FV]
[PV] [STO] [i]
NG [N]
0 [PV]
1 [PMT]
[FV] [STO] [PMT]
NP [N]
I% [i]
0 [FV]
[PV] [STO] 0

NG [N]
G% [i]
1 [PV]
0 [PMT]
[FV] STO [PMT]
N NG NP * - [N]
I% [i]
0 [PV]
[FV]
N [N]
0 [PMT]
[PV]

[RCL] 0 [-] PV [X<>Y] [/]

An example:
Suppose you need to determine the initial payment for the following Mortgage:

N: 360 - number of payments (30 years, 12 payments per year)
PV: 60000 - present value
I%: 1 - periodic rate (annual rate I%YR=12 divided by NP=12)
NP: 12 - number of payments per growth period (a year)
G%: 7.5 - growth rate per growth period
NG: 5 - number of growth periods = number of times the payment grows

[f] [CLEAR FIN]
[g] [END]

12 [N]
1 [i]
[STO] [PMT]
-7.5 [FV]
[PV] -> -4.599208284 [STO] [i]
5 [N]
0 [PV]
1 [PMT]
[FV] -> -4.560749934 [STO] [PMT]
12 [N]
1 [i]
0 [FV]
[PV] -> 51.33159384 [STO] 0

5 [N]
7.5 [i]
1 [PV]
0 [PMT]
[FV] -> -1.435629326 STO [PMT]
300 [N]
1 [i]
0 [PV]
[FV] -> 2697.327316
360 [N]
0 [PMT]
[PV] -> -75.03071565

[RCL] 0 [-] 60000 [X<>Y] [/] -> -474.8251297 is the initial payment.

A bit more involved, but less keystrokes ;-)

Cheers, Werner