DM41X: Interest Rate of a Forward-Forward Agreement

DM41X: Interest Rate of a Forward-Forward Agreement

A Future Interest Contract: Forward-Forward Agreement

A forward-forward agreement (yes, forward-forward is not a typo, that is what’s really called) is a financial transaction which starts on a forward date and ends on another forward date. An example transaction involves one party borrowing a sum amount to be paid back, only at the same time to deposit such amount in another short-term investment. The forward-forward rate, which I designate as FFR, is combined interest rate taking both transactions at the same time. The FFR is calculated as such:

FFR = [ (1 + IL * DL ÷ 365) ÷ (1 + IS * DS ÷ 365) – 1 ] * (365 ÷ (DL – DS))

IL: interest rate for the longer period, in decimal

DL: length of the long period

IS: interest rate for the shorter period, in decimal

DS: length of the short period

365: number of days in a year. It gets replaced with 360 if a 30/360 year is used.

If the loan lasts longer, the FFR represents the interest cost.

If the deposit lasts longer, the FFR represents the interest earned.

DM41X and HP 41C Code: FFR

01 LBL T^FFR

02 ^T FWD-FWD RATE

03 AVIEW

04 PSE

05 ^T LONG TRM DYS?

06 PROMPT

07 STO 01

08 STO 06

09 ^T LONG TRM %?

10 PROMPT

11 STO 02

12 %

13 365

14 /

15 1

16 +

17 STO 05

18 ^T SHORT TRM DYS?

19 PROMPT

20 STO 03

21 ST- 06

22 ^T SHORT TRM %?

23 PROMPT

24 STO 04

25 %

26 365

27 /

28 1

29 +

30 ST/ 05

31 RCL 05

32 1

33 -

34 365

35 *

36 RCL 06

37 /

38 2

39 10↑X

40 *

41 STO 07

42 ^T FFR=_

43 ARCL 07

44 AVIEW

45 RTN

Notes:

^T: It starts an alpha string.

Line 42: ^T FFR+_: The underscore is used as a space

Alpha strings are abbreviated in attempt for the message to fit the screen without scrolling.

Periods are assumed to be one year or less, and a 365-day year is assumed.

Examples

Example 1:

Longer Period (borrow): 49 days, 11%

Shorter Period (deposit): 30 days, 8%

Result: FFR= 15.6340

Example 2:

Longer Period (borrow): 63 days, 10.2%

Shorter Period (deposit): 31 days, 11.1%

Result: FFR= 9.2410

Source

Steiner, Bob. Mastering Financial Calculations. Second Edition. Prentice Hall: Financial Times. 2007. ISBN 978-0-273-70444-7. pp. 68-70

Eddie

All original content copyright, © 2011-2026. Edward Shore. Unauthorized use and/or unauthorized distribution for commercial purposes without express and written permission from the author is strictly prohibited. This blog entry may be distributed for noncommercial purposes, provided that full credit is given to the author.

RPN: Absolute Value Equations with the HP 11C and DM41X

RPN: Absolute Value Equations with the HP 11C and DM41X

Introduction: Solving |z * w + y| = x

Today’s blog focuses on solving the absolute value equation:

|z * w + y| = x

for the variable w, and the values of z, y, and x are given and are on the Classic RPN stack.

For example, in the problem |5 * w + 7| = 2, the stack would be set up as:

t: (anything, it doesn’t matter)

z: 5

y: 7

x: 2

(This is why I set the variable as w instead of the usual x.)

One approach is to use memory registers and other uses only stack operations. Today’s algorithm focuses on the latter.

Caution: In the above equation, x will always be non-negative. The equation will never be valid if x is negative.

The Algebra

Solve for w:

|z * w + y| = x

This leads us to solve the two equations:

(I)

z * w + y = -x

z * w = -x – y

w = -x/z – y/z

Let w- = -x/z – y/z = (-x/z) + (-y/z)

(II)

z * w + y = x

z * w = x – y

w = x/z - y/z

Let w+ = x/z – y/z = (x/z) + (-y/z)

Then:

w- = -x/z – y/z

w- = (-x/z) + (-y/z)

w- = (-x/z) + (-y/z) + (-x/z) + (x/z)

w- = 2 * (-x/z) + (x/z) + (-y/z)

w- = 2 * (-x/z) + w+

RPN Code: HP 11C (adoptable for other RPN calculators)

LBL A	001	42, 21, 11	Program start
R↓	002	33
R↓	003	33
X<>Y	004	34
R↓	005	33
1/x	006	15
×	007	20
LST x	008	43, 36
X<>Y	009	34
R↓	010	33
×	011	20
LST x	012	43, 36
R↑	013	43, 33
X<>Y	014	34
R↓	015	33
X<>Y	016	34
CHS	017	16
X<>Y	018	34
+	019	40
ENTER	020	36
ENTER	021	36
LST x	022	43, 36
-	023	30
LST x	024	43, 36
-	025	30
RTN	026	43, 32	Program end

RPN Code: DM41X (HP 41C series, no module is required)

LBL “ASBEQ”

RDN

RDN

X<>Y

RDN

1/x

×

LAST X

X<>Y

RDN

×

LAST X

R↑

X<>Y

RDN

X<>Y

CHS

X<>Y

+

ENTER

ENTER

LAST X

-

LAST X

-

RTN

Notes:

* RDN is shown as R↓

* To enter R↑, press XEQ, ALPHA, R, SHIFT, ENTER, ALPHA

Subroutines Used

We used several techniques to manipulate the stack. They are presented below:

Rotate stack from X, Y, Z, T to Z, X, Y, T

R↓

R↓

X<>Y

R↓

Source:

Ball, John A. Algorithms for RPN Calculators John Wiley & Sons: New York. 1978. ISBN 0-471-03070-8. pg. 78

Multiply Y and Z by 1/X. Stack: X, Y, Z, T → X, Y/X, Z/X, T

1/x

×

LAST X

X<>Y

R↓

×

LAST X

R↑

X<>Y

Change X, Y to Y+ X, Y – X

+

ENTER

ENTER

LAST X

-

LAST X

-

The resulting stack is:

z

z

y + x

y – x

Doing LAST X, -, twice is effectively subtracting whatever is in L register twice.

Examples

|4 * w – 6| = 5

Stack:

z: 4

y: -6

x: 5

Results:

y: 2.75

x: 0.25

|2 * w + 5| = 3

Stack:

z: 2

y: 5

x: 3

Results:

y: -1

x: -4

Eddie

All original content copyright, © 2011-2026. Edward Shore. Unauthorized use and/or unauthorized distribution for commercial purposes without express and written permission from the author is strictly prohibited. This blog entry may be distributed for noncommercial purposes, provided that full credit is given to the author.

RPN Calculators: INPUT vs PROMPT

RPN Calculators: INPUT vs PROMPT

Later RPN keystroke programming calculators are able to display alphabetic messages and store to variables for alphabetic names.

HP 32S, HP 32SII, HP 33S, HP 35S, DM32	HP 41C (all variants), DM41X	HP 42S, DM42, DM42n, Free 42
Single letter variable names	Numeric-named variables only	Both numeric-named variables and alphabetic (and alphanumeric) variable names. Alphabetic and alphanumeric named variables are enclosed in quotes (alpha strings) well stored and recalled and take additional memory.
Can display messages by setting Flag 10 and using the equation feature to type messages	Can display messages and prompts	Can display messages and prompts

Two common ways to cue the user to enter values are the INPUT and PROMPT commands.

The INPUT Command: HP 32 and HP 42S (and Swiss Micros/emulator equivalents)

Note: The INPUT command is not available in the HP 41C’s command set.

General syntax: INPUT var

When an INPUT command is encountered, the screen will display [var]?= on the X stack.

Example:

INPUT R displays R? [previous value stored in R]

HP 32 Family: The variable is a single-letter name or the indirect variable i.

HP 42S Family: A custom alpha variable, a numeric-named variable (i.e. 00, 01, 02, etc.), indirect variables, or the stack levels X, Y, T, Z, or L (last argument).

The INPUT has the double benefit of storing whatever is entered into the variable asked for. INPUT will also show the previously stored value, so we can just accept it by pressing R/S to keep the old value.

Example: Volume of a Cone

HP 32 family

HP 42S family

V01 LBL V V02 INPUT R V03 INPUT H V04 π V05 RCL R V06 x^2 V07 × V08 RCL H V09 × V10 3 V11 ÷ V12 RTN No quotes are needed for alphabetic variables.

00 {30-Byte Prgm } 01 LBL “VCONE1” 02 INPUT “R” 03 INPUT “H” 04 PI 05 RCL “R” 06 x↑2 07 × 08 RCL “H” 09 × 10 3 11 ÷ 12 RTN We could use variables 00 and 01 (for example) for radius and height, respectively, except the input command prompt will show “R00?” or “R01?” which may not be user-friendly. The INPUT does not replace the contents of the alpha register. If we want the alphanumeric/alphanumeric variables (“R”, “H”) to be erased, we could have inserted CLV “R” and CLV “H” at the end, but that will erase the value associated with them.

The PROMPT Command: HP 41C and HP 42S (and Swiss Micros/emulator equivalents)

Note: The PROMPT command is not available on the HP 32S family.

General Syntax:

“alpha string”

PROMPT

STO var

The alpha string is displayed until something, usually a numeric value, is entered. Unlike the INPUT command, the PROMPT does not automatically store the entered value into a variable. Therefore, if you want to use the value for future use, a STO (store) command must be used following the prompt.

Let’s take our volume of the cone example again:

HP 41C family	HP 42S family
01 LBL “VCONE2” 02 ^T RADIUS? 03 PROMPT 04 STO 00 05 ^T HEIGHT? 06 PROMPT 07 STO 01 08 PI 09 RCL 00 10 X↗2 11 * 12 RCL 01 13 * 14 3 15 / 16 RTN R00 = radius R01 = volume	00 { 40-Byte Prgm } 01 LBL “VCONE2” 02 “RADIUS?” 03 PROMPT 04 STO 00 05 “HEIGHT?” 06 PROMPT 07 STO 01 08 PI 09 RCL 00 10 X↑2 11 × 12 RCL 01 13 × 14 3 15 ÷ 16 RTN R00 = radius R01 = volume With PROMPT, I like to use the numeric-named memory registers, but we can use alphabetic or alphanumeric registers as well.

HP 32SII/DM32: Simulating PROMPT with Flag 10

Even though the HP 32SII does not have a PROMPT command, we can kind of simulate it by using the equation message feature.

To set flag 10: [ |→ ] [ × ]* (FLAGS), { SF }. [ . ] [ 0 ]

To clear flag 10: [ |→ ] [ × ]* (FLAGS), { CF }. [ . ] [ 0 ]

We have to use the decimal point key in order to access flags beyond 9.

(*HP 35S: [ ←| ] [ ↑ ] (FLAGS))

HP 32SII/33S/35S/DM32
W01 LBL W W02 SF 10 W03 “=RADIUS” W04 STO R W05 “=HEIGHT” W06 STO H W07 CF 10 W08 π W09 RCL R W10 x^2 W11 × W12 RCL H W13 × W14 3 W15 ÷ W16 RTN	Turn message mode on Enter as an equation =RADIUS Enter radius and press [R/S] Enter as an equation =HEIGHT Enter height and press [R/S] Turn message mode off, so equations can operate normally

Note: Equations are NOT on the original HP 32S.

I hope you find this helpful.

Eddie

All original content copyright, © 2011-2025. Edward Shore. Unauthorized use and/or unauthorized distribution for commercial purposes without express and written permission from the author is strictly prohibited. This blog entry may be distributed for noncommercial purposes, provided that full credit is given to the author.

The author does not use AI engines and never will.