(29C) Accurate TVM for HP-19C/HP-29C

[Jeff_Kearns]

The HP-29C does not have the HP SOLVE functionality of later models starting with the HP-34C and implemented in the HP-15C, HP-41 Advantage module. This program combines the Equation Solver for the HP-19C/HP-29C published by Stefan Vorkoetter in the old software library with the accurate TVM code used in the HP-34C program, which does not have Recall Arithmetic, into a 71 line program effectively turning your HP-29C into a reliable financial calculator (insofar as standard TVM calculations are concerned).

Code:


LINE     KEYSTROKES      COMMENTS

 01      g LBL 0         -main entry point
 02      STO 0           -store index of variable to solve for
 03      roll dn
 04      STO .2          -store second guess
 05      roll dn
 06      STO .1          -store first guess
 07      STO i           -compute f1 = f(R1,..,Ri1,..,Rn)
 08      GSB 9
 09      STO .0
 10      RCL .2          -compute f2 = f(R1,..,Ri2,..,Rn)
 11      STO i
 12      g LBL 1
 13      GSB 9           -the equation to be solved must begin at LBL 9
 14      STO .2
 15      RCL .1          -compute Ri2 <- (Ri1 f2 - Ri2 f1) / (f2 - f1) 
 16      x
 17      RCL i 
 18      STO .1          -move old Ri2 to Ri1 while we're here
 19      RCL .0
 20      x
 21      -
 22      RCL .0
 23      RCL .2
 24      STO .0          -move old f2 to f1 while we're here 
 25      x<>y 
 26      - 
 27      / 
 28      STO i            -save new value for Ri2 
 29      RCL .1           -compare to previous guess 
 30      X≠Y              -keep going until they're the same
 31      GTO 1
 32      g RTN            -end of SOLVER routine that can be used with any MISO equation
 33      g LBL 9          -begin entering TVM equation at this step
 34      RCL 2
 35      EEX
 36      2
 37      ÷
 38      ENTER
 39      ENTER
 40      1
 41      +
 42      LN
 43      X<>Y
 44      LSTx
 45      1
 46      X≠Y
 47      -
 48      ÷
 49      *
 50      RCL 1
 51      *
 52      e^x
 53      RCL 3
 54      X<>Y
 55      *
 56      LSTx
 57      1
 58      -
 59      RCL 4
 60      *
 61      EEX
 62      2
 63      RCL 2
 64      ÷
 65      RCL 6
 66      +
 67      *
 68      +
 69      RCL 5
 70      +
 71      RTN

Usage instructions:

1. Store 4 of the following 5 variables as follows, using appropriate cash flow conventions:

N STO 1 --- Number of compounding periods
I STO 2 --- Interest rate (periodic) expressed as a %
B STO 3 --- Initial Balance or Present Value
P STO 4 --- Periodic Payment
F STO 5 --- Future Value
and store the appropriate value (1 for Annuity Due or 0 for Regular Annuity) as
B/E STO 6 --- Begin/End Mode. The default is 0 for regular annuity or End Mode.

2. Leave the floating variable un-stored, but enter two guesses (if desired), each followed by the ENTER key; and

3. Enter the floating variable register number followed by GSB 0

Example from the HP-15C Advanced Functions Handbook-

"Many Pennies:

A corporation retains Susan as a scientific and engineering consultant at a fee of one penny per second for her thoughts, paid every second of every day for a year.
Rather than distract her with the sounds of pennies dropping, the corporation proposes to deposit them for her into a bank account in which interest accrues at the rate of 11.25 percent per annum compounded every second. At year's end these pennies will accumulate to a sum

total = (payment) X ((1+i/n)^n-1)/(i/n)

where payment = $0.01 = one penny per second,
i = 0.1125 = 11.25 percent per annum interest rate,
n = 60 X 60 X 24 X 365 = number of seconds in a year.

Using her HP-15C, Susan reckons that the total will be $376,877.67. But at year's end the bank account is found to hold $333,783.35 . Is Susan entitled to the $43,094.32 difference?"

31,536,000 STO 1
(11.25/31,536,000) STO 2
0 STO 3
-0.01 STO 4

5 GSB 0

The HP-29C gives the correct result: $333,783.35.