The Resource Magazine For Apple, Atari, and Commodore ...

36 COMPUTE! September/October. 198O. Issue 6
pose you are paying on a loan whose balance is BAL,
using equal monthly payments called PMT, and you
have N payments yet to make. What is the
equivalent simple interest rate, called the APR, of
your loan? The equation relating these quantities is
BAL = PMT((1 - (1 +I)-N)/I) (9)
.
Table 5. Results of the program in Listing 4.
XL = 0.3, XR = 0.4 XL m 2.0. XR = 2.2
XM
0.35
0.375
0.3625
0.35625
0.359375
0.3578125
O.357O3125
0.357421875
0.357226563
0.357324219
0.357373047
0.357397461
0.357409668
0.357403565
0.357400513
0.357402039
0.357402802
0.357403183
0.357402993
0.357402897
XM
2.1
2.15
2.175
2.1625
2.15625
2.153125
2.1546875
15:390625
15351563
15332032
15322266
15327149
2.15329590
2.15328369
2.15328980
2.15329285
2.15329132
2.15329209
2.15329247
2.15329228
Appendix B.
The method of interval halving will not work in the
SOmewhal unusual case of a double root to a polynomial
equation. For example, il ;i factor nl a polynomial equation
is
(x - 1)2 = X2 - 2x + 1 = 0)
then the solution at x = i cannot be found with interval
halving.
Appendix C.
One nl the most popular iterative techniques is known
as Newton's method or the Newton-Raphson method. It
wits not mentioned here because ii requires a knowledge
of calculus. The iterative formula is;
xj + 1 = x{ - F(x)/Fl(ii)
where ii is assumed thai the equation is initially in the
form F(x) = 0.
Note that in Equation (9), I is the monthly interest
rale, and it must be multiplied by 1200 to convert it
to an annual rate expressed in a percent form. In
any case, I challenge you to solve Equation (9) by
straightforward, direct techniques. Refer to the
July/August issue of COMPUTE, for a solution of this
equation by interval halving.
I would like to conclude this article by saying
that you have only seen the tip of the iceberg as far
as numerical analysis is concerned. One of the best
elementary texts on this subject is Peter A. Stark's
INTRODUCTION TO NUMERICAL
METHODS, Macmillian. 1970. Note that many
techniques require a knowledge of calculus. You may
want to check your library for textbooks on the sub
ject. One last plea: if you are a high school student
who is planning a career in computer science, please
get all of the courses in mathematics that your school
offers. Although you do not have to be a
mathematical genius to work in the computer field,
every tool in the old toolbag will be helpful.
PET and APPLE II Users
PASCAL
ABACUS Software makes available its version of TINY PASCAL for
the users of two of the most popular personal computers.
TINY PASCAL is a subset of the standard PASCAL as defined by
Jensen and Wirth. It includes the structured programming
features: IF-THEN-ELSE. REPEAT-UNTIL, FOR TC"'DOWN TO-DO.
WHILE-DO, CASE-OF-ELSE, FUNC and PROC. Now you can learn the
language that is slated to become the successor to BASIC.
TINY PASCAL is a complete package that allows you to create,
compile and execute progams written in the PASCAL language.
You can save source and object code on diskette or cassette (PET
version only). Comprehensive user's manual included. The manual
can be examined for $10 (refundable with software order).
REQUIREMENTS
PET 16K/32K New ROMS cassette $40
PET 16K/32K New ROMS diskette $35
Apple II 32K Applesoft ROM w/DOS $35
Apple II 48K Applesoft RAM w/DOS $35
TINY PASCAL User's Manual $10
6502 Interpreter Listing $20
master charge
FREE postage in U.S. and CANADA
All orders prepaid or COO
Appendix A.
The method of successive substitutions is guaranteed to
converge to an answer if
lF'(x)M