akcs.kevin@hpcvbbs.UUCP (Kevin Jessup) (04/25/91)
I have recently received a few net-mail requests for
this baby so I am posting it once again.
******************************************************
Documentation file for an HP48SX
Time Value of Money Equation
Kevin P. Jessup
April 25, 1991
******************************************************
INTRODUCTION
------------
HP48SX owners that also have the equation library card
have available to them a time value of money (TVM)
equation solver. This software is a quick attempt to
make a similar package available to those who do not
have the card. I am not sure how closely this equation
emulates the technique used in the equation library
card but it does appear to give equivalent results.
The program is based on the TVM equations that were used
in the PPC ROM for the HP41. The equations used there
were adapted by me for use on the HP48. The original
authors of the PPC ROM version were Graeme Dennes and
Don Dewey.
While the user interface is not quite as good as that
used by the equation library card, I find it adequate.
The equation used here also allows you to set different
compounding and/or payment frequencies. This is typical
of European and Canadian Mortgages.
Documentation and a few examples follow. The "ASC encoded"
directory appears after the examples. Let me know if you
have any trouble. Please feel free to modify, enhance or
correct any errors in this package as you see fit.
Loading
-------
Transfer the TVM file to your 48. Run the ASC-> utility
to convert the string to a directory. Store the directory
as TVM. Verify the following...
Checksum: # 96A8 (hex)
Byte count: 996
OPERATION
---------
First, go to the TVM directory. To start, simply
hit [LEFT SHIFT] [SOLVE] then [SOLVR] to enter the
equation solver application.
The proper equation is already named and stored
under EQ. In case you accidentally wipe it out,
it is duplicated under the name TVM.
Do not store any other equations, programs or variables
in this directory so as to avoid conflicts with the
TVM operations.
KNOWLEDGE OF THE HP48SX SOLVER AND TIME VALUE OF MONEY
TRANSACTIONS IS ASSUMED!!
In the following examples and indeed, for all equation
solver inputs and outputs as used here, money received by
you is positive. Money payed out is negative.
Equation variables
------------------
N = Number of periods
I = % nominal interest rate for the period implied
by the compounding and payment frequencies.
If the payment frequency (PF) and compounding
frequency (CF) equal 12, this becomes the annual
percentage rate (APR).
PV = Present Value
PMT = Periodic payment
FV = Future Value
CF = Compounding Frequency
PF = Payment Frequency
TVM equation control keys
-------------------------
BEG = Sets BEGIN mode (payments due at beginning of period).
END = Sets END mode (payments due at end of period).
RESET = Sets END mode and sets N, PF and CF equal to 12.
All other variables are cleared! Again, note
that I (% interest) now functions as APR (annual
percentage rate).
Example 1
---------
Find the annual simple interest rate (%) for a
$1000 loan to be repayed after one year with a
single payment of $1187.50.
ENTER THIS HIT THIS KEY SEE THIS
---------- ------------ --------
RESET END mode
N=PF=CF=12
1000 PV PV: 1000
-1187.5 PMT PMT: -1187.5
1 N N: 1
NXT
1 CF cf: 1
1 PF pf: 1
NXT
[LEFT SHIFT] I Solving for I
I: 18.75
The interest rate is 18 and 3/4 percent. That should
have been obvious. Now let's try some examples that
are a bit more involved.
Example 2
---------
$2000 is placed in a savings account that earns 5.25%
interest compounded monthly. What is its value after
5 years (5 * 12 = 60 periods)?
ENTER THIS HIT THIS KEY SEE THIS
---------- ------------ --------
RESET END mode
N=PF=CF=12
-2000 PV PV: -2000
5.25 I I: 5.25
60 N N: 60
[LEFT SHIFT] FV Solving for FV
FV: 2598.8645319
The account made $598.86 in interest.
Example 3
---------
A mortgage of $150,000 is to be fully amortized at 12%
interest compounded monthly. If end of period payments of
$1600.00 are to be made, how many payments will be required?
ENTER THIS HIT THIS KEY SEE THIS
---------- ------------ --------
RESET END mode
N=PF=CF=12
12 I I: 12
150000 PV PV: 150000
0 FV FV: 0
-1600 PMT PMT: -800
[LEFT SHIFT] N Solving for N
N: 278.64
The loan will be payed in 278.64 months or about 23 years.
Example 4 (Canadian Mortgage)
-----------------------------
Find the monthly end of period payments required
to fully amortize a 25 year (25 * 12 = 300 periods)
$85,000 loan at 11% compounded semiannually.
ENTER THIS HIT THIS KEY SEE THIS
---------- ------------ --------
2 NXT CF cf: 2
300 NXT N N: 300
11 I I: 11
85000 PV PV: 85000
[LEFT SHIFT] PMT Solving for PMT
PMT: -818.15
Example 5
---------
What is the future value of $100 biweekly savings
(26 periods/year) of $100 for 3 years at a nominal
annual rate of 5.5% compounded daily. Payments
are to be made at the start of each period.
ENTER THIS HIT THIS KEY SEE THIS
---------- ------------ --------
RESET END mode
N=PF=CF=12
NXT BEG BEGIN mode
365 CF cf: 365
26 PF pf: 26
78 NXT N N: 78
5.5 I I: 5.5
-100 PMT PMT: -100
[LEFT SHIFT] FV Solving for FV
FV: 8489.32
Example 6
---------
You wish to finance the purchase of a new car with
a 3-year loan at 10.5% APR. You will require a loan
in the amount of $8,750.00. What will your monthly
payments be?
ENTER THIS HIT THIS KEY SEE THIS
---------- ------------ --------
RESET END mode
N=PF=CF=12
35 N N: 36
10.5 I I: 10.5
8750 PV PV: 8750
[LEFT SHIFT] PMT Solving for PMT
PMT: -284.40
"ASC encoded" directory
-----------------------
[CUT HERE]
%%HP: T(3)A(R)F(.);
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9200000000000000000D100020646520339200000000000000000D1000109410
339200000000000000000B10003005D445303392000000000000000008A69"
[CUT HERE]
The HP48SX utilities "ASC->" and "->ASC" were written by
Dr. Bill Wickes and are available at various ftp sites and
are proabaly on the net.
Kevin Jessup
9118 North 85th Street
Milwaukee, WI 53224
Data line: (414)362-2020 (Milwaukee HP48SX BBS)