(12C) Mortgage Loan Interest Rate
06-15-2021, 07:45 AM (This post was last modified: 06-15-2021 07:58 AM by Gamo.)
Post: #1
 Gamo Senior Member Posts: 725 Joined: Dec 2016
(12C) Mortgage Loan Interest Rate
This program was modify and adapted to work for the HP-12C from
HP-33E Applications Book on Page 37

As state in this book program will calculate the interest rate on a loan
with equal periodic payments. The user must specify the number of period,
the present value or initial loan amount, and the payment amount.

The program performs an iterative solution for [i] using Newton's method.

Usually this type of problem can be solve easily with the HP-12C but I found
that this program run faster than the Original HP-12C when solve for "Interest Rate"

So this program is use to try out the computation speed between the build-in TVM
functions and the custom program.
-----------------------------------------------------------------
Example Problem:
n = 36
PV = 3600
PMT = -360
Interest Rate = ?

[f] 2
36 [n]
3600 [PV]
360 [CHS] [PMT]
[i] ...... about 17 second display 9.64

To use program: same data as previous problem
press [R/S]....... about 12 second display 9.64
----------------------------------------------------------------
Program:
Code:
 01 RCL [n] 02 STO 1 03 RCL [PV] 04 RCL [PMT] 05  ÷ 06 STO 3 07  0 08 X<>Y 09 X≤Y 10 CHS 11 ENTER 12 1/x 13 X<>Y 14 RCL 1 15 ENTER 16  x 17  ÷ 18  - 19 STO 2 20 RCL 3 21 0 22 X<>Y 23 X≤Y 24 CHS 25 RCL 2 26  x 27  1 28 RCL 2 29  1 30  + 31 RCL 1 32 CHS 33 Y^X 34 STO 5 35  - 36  - 37 RCL 1 38 RCL 2 39 1/x 40  1 41  + 42  ÷ 43  1 44  + 45 RCL 5 46  x 47  1 48   - 49 RCL 2 50  ÷ 51  ÷ 52 STO+2 53  0 54 X<>Y 55 X≤Y 56 CHS 57 EEX 58  6 59 CHS 60 X≤Y 61 GTO 20 62 RCL 2 63 EEX 64  2 65  x

Remark:
This program speed don't make noticeable different on the HP-12C+

I think the reason that this program run faster might be how this program use
the initial guess (The guess migh be very close to the solution than the HP-12C TVM algorithm)

Gamo 6/2021
06-15-2021, 01:13 PM
Post: #2
 Albert Chan Senior Member Posts: 2,494 Joined: Jul 2018
RE: (12C) Mortgage Loan Interest Rate
(06-15-2021 07:45 AM)Gamo Wrote:  [f] 2
36 [n]
3600 [PV]
360 [CHS] [PMT]
[i] ...... about 17 second display 9.64

To use program: same data as previous problem
press [R/S]....... about 12 second display 9.64

It seems HP12C use whatever was stored in [i] as guess.
If we provide same guess of program for HP12C TVM:

(-PMT/PV) - (-PV/PMT)/N² ≈ 1/10 - 10/36² ≈ 9.23%

9.23 [i] [i] ... finished in 10 second

Solve again, with true rate as guess

[i] [i] ... finished in 4 second

With 5% guess, and interrrupt rate search, we get this:

5 [i] [i] [On] [On] ﻿ ﻿ ﻿ → 8.99
﻿ ﻿ ﻿ [i] [i] [On] [On] ﻿ ﻿ ﻿ → 9.62
﻿ ﻿ ﻿ [i] [i] [On] [On] ﻿ ﻿ ﻿ → 9.64
06-16-2021, 06:00 AM
Post: #3
 Gamo Senior Member Posts: 725 Joined: Dec 2016
RE: (12C) Mortgage Loan Interest Rate
According to this book state that

The initial guess for [i] is given by

i₀ = |PMT ÷ PV| - (1 ÷ n²) |PV ÷ PMT|

Gamo
06-16-2021, 03:28 PM
Post: #4
 Albert Chan Senior Member Posts: 2,494 Joined: Jul 2018
RE: (12C) Mortgage Loan Interest Rate
Timing suggested solving for i is using IRR routine.

Clear Reg
3600 CF0 ﻿ ﻿ ﻿ ﻿ ﻿ ﻿ ; PV
360 CHS CFj﻿ ﻿ ; PMT
36 Nj ﻿ ﻿ ﻿ ﻿ ﻿ ﻿ ﻿ ﻿ ﻿ ﻿ ﻿ ﻿; N
IRR ﻿ ﻿ ﻿ ﻿ ﻿ ﻿ ﻿ ﻿ ﻿ ﻿ ﻿ ﻿ ﻿ ﻿ ; 9.635443543 (17 sec)

9.23 [i] RCL [g] [R/S] ; guess = (-PMT/PV) - (-PV/PMT)/N^2 (10 sec)
﻿ ﻿ ﻿ ﻿ ﻿ ﻿ ﻿ [i] RCL [g] [R/S] ; guess = true rate (4 sec)
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