?Rounding errors?

[Mel Bishop]

Originally posted by Paul Dixon:
the problem is the line...

Okay, let me do some razzle-dazzle and see what I come up with.
I'll let you know. Thanks.


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[Paul Dixon]

Mel,
the problem is the line :

payment = int(te * 100 + .5) / 100


te is calculated as $454.2312

The above line makes this int(45423.62)/100 = $454.23

This is less than the 454.2312 needed to repay the loan on time so there is a shortfall of $0.0012 per month. This accumulates to give the 361st payment.

You need to change the above line so that the repayment is ALWAYS higher (rounded up to the nearest cent) than the exact figure required to pay off the loan on time.
What you're doing is rounding to the nearest cent even if that means rounding down.. which will then leave a shortfall.

Paul.


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[Mel Bishop]

I'm not refusing to post my code. I simply would prefer not to
if I don't have to. Here is what I have so far. The program
isn't finished. I would like to find out where the rounding
errors are before I go on to future things.

	$lib all off
	color 14,1

        do
        cls
        f$ = "$###,###.##"

        locate  5,29 : Print;"Regular payment on a loan"

	locate  7,25 : Input;"Term in years: ",years
        if years = 0 then exit loop

        locate  9,25 : Input;"    Principal: ",principal
        if principal = 0 then exit loop

        save = principal
        locate 11,25 : Input;"Interest rate: ",interest
        if interest = 0 then exit loop
        monthly = 12				'Monthly payments

REM	Computer monthly payments
        te = ((interest / 100) * principal / monthly) / _
             (1-1 / ((interest / 100) / monthly + 1) ^ (monthly * years))

        payment = int(te * 100 + .5) / 100


[b]
REM     This is the mod that I came up with in response to Pauls
REM     response. It seems to work in as far as making the 
REM     months come out exact.

        te$ = str$(te)
        p = instr(te$,".")
        if p = 0 then te$ = te$ + ".000"

        te = val(mid$(te$,p+3,1))
        if te < 5 then payment = payment + .01
[/b]
rem
        t$ = using$(f$,payment)
        t$ = remove$(t$," ")
        locate 15,22 : print;"Regular payments: ";t$

        locate 17,10
        print;"Press ESCape to end the program or any other key to"
        locate 18,10
        print;"write the data to a disk file."

        if abort = 0 then

        fi$ = "amort.txt"
        te$ = dir$(fi$)
        if te$ <> "" then kill fi$

        open fi$ for binary as #1
        crlf$ = chr$(13) + chr$(10)
        separator$ = string$(75,"-") + crlf$

        m$ = "Original loan amount: " + using$(f$,principal) + crlf$
   m$ = m$ + "      Length of loan: " + Str$(years) + " Years" + crlf$
   m$ = m$ + "       Interest Rate: " + str$(interest) + " Percent" + crlf$
   m$ = m$ + crlf$
   m$ = m$ + "     Monthly Payment: " + using$(f$,payment)
   m$ = m$ + crlf$ + crlf$

	put$ #1,m$
	put$ #1,separator$
	put$ #1,"Month"      + space$(5)
	put$ #1,"Interest"   + space$(5)
	put$ #1,"Principal"  + space$(8)
	put$ #1,"Balance"    + space$(7)
	put$ #1,"Equity"     + space$(5)
        put$ #1,"Accr Inter" + crlf$

	put$ #1,separator$

        for month = 1 to monthly * years + 5

REM	Calculate interest paid with each payment
	tointerest = int((principal * (interest / 100) / monthly) * 100 + .5) / 100

REM	Add up the accumulated interest
	accum = accum + tointerest

REM     How much of the payment goes to principal
        toprincipl = payment - tointerest

REM     How much equity is built up
	equity = equity + toprincipl
        if equity > save then equity = save

REM     How much of the principal is left
        principal  = principal - toprincipl

REM	Zero out a negative number
        if principal < 0 then principal = 0

        t1$ = using$(f$,tointerest) : t1$ = remove$(t1$," ")
        t2$ = using$(f$,toprincipl) : t2$ = remove$(t2$," ")
        t3$ = using$(f$,principal)  : t3$ = remove$(t3$," ")
        t4$ = using$(f$,equity)     : t4$ = remove$(t4$," ")
        t5$ = using$(f$,accum)      : t5$ = remove$(t5$," ")

        te$ = space$(2) + using$("###",month)
        te$ = te$ + space$(13 - len(t1$)) + t1$

        for x = len(te$) to 31 - len(t2$)
        te$ = te$ + " "
        next x

	te$ = te$ + t2$
        for x = len(te$) to 46 - len(t3$)
        te$ = te$ + " "
        next x
	te$ = te$ + t3$

        for x = len(te$) to 59 - len(t4$)
        te$ = te$ + " "
        next x
        te$ = te$ + t4$

        for x = len(te$) to 74 - len(t5$)
        te$ = te$ + " "
        next x
        te$ = te$ + t5$

	put$ #1,te$ + crlf$
rem	print;te$
        if principal <= 0 then exit for
        if month / 12 = int(month / 12) then
        put$ #1,string$(75,"-") + crlf$
        end if
        next month
        close #1

	m$ = "Finished writing to " + chr$(34) + "AMORT.TXT" + chr$(34)
        m$ = m$ + " file."
        col = 40 - int(len(m$) / 2)
        locate 20,col : print;m$;

REM     I didn't include an LPRINT routine since a lot of printers
REM     are of the USB variety. Can't get there from here.

        m$ = "Bring up your favorite ASCII word processor to print it out."
        col = 40 - int(len(m$) / 2)
        locate 21,col
        print;m$;

        end if

        m$ = "Tap ESCape to end or any other key to compute another"
        col = 40 - int(len(m$) / 2)
        locate 22,col
        print;m$

        t = abort
        if t = 1 then exit loop
        loop

        end

function abort
	while instat=0:wend
        an$ = inkey$
        if an$ = chr$(27) then
        function = 1
        else
        function = 0
        end if
        end function

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[This message has been edited by Mel Bishop (edited August 03, 2004).]

[Michael Mattias]

> it seems to be with the ?rounding errors? in the calcuations

since you refuse to post even a piece of code (fwiw, amortization is hardly a trade secret), just check your data types.

if float? you have rounding problems, and you must handle them.

you have it easy, because you know about the need to round your floats.

i had it a little tougher because i had to find a little problem in the compiler first:

http://www.powerbasic.com/support/pb...ad.php?t=24241

(fwiw, there's some rounding code in there you can probably use).

[Mel Bishop]

Thanks for the tips MM but no go. There's nothing wrong with
the loop counters. They work as advertised. It seems to be
with the ?rounding errors? in the calcuations.

If anyone has a commercial loan program, could you please enter
the following values and see if it bleeds over to 361 months on
your program.

Loan amount: $80,000
Term: 30 years (360 months)
Interest: 5.5 percent APR

This bleed over doesn't happen all the time. Just occasionally.


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[Michael Mattias]

You might also consider changing to the FIX datatype with FIXDIGITS=4, which gives you the equivalent of a CURRENCY datatype... which of course is perfect for money calculations.

[Michael Mattias]

Check all loop counters (FOR...NEXT) and WHILE/DO..WHILE|UNTIL.

Make sure all 'end of loop' conditions are integer; or, the 'done with the loop' comparison is made against a difference, like:

  DO UNTIL ABS(lastval# - thisval#) < .00001!

.. or something like that.

Hopefully, you have not written too much code using something like..

  IF Z# < | > |= X# THEN
     [b]EXIT FOR[/b]
     ....

.. because then you'll have to go through your code line-by-line looking for any statement in which you do a numeric comparison of non-integers.

MCM

[Mel Bishop]

Because of a recent post, I decided to dust off and polish up
an old loan amortization program that I wrote some years ago.
Now to the best of recollation, the old program, written in
PB/DOS 2.1f was accurate down to the penny right up to the last
month of the repayment period.

With PB/DOS 3.5, under certain circumstances, an error occurs
that I haven't been able to narrow down.

For example, if I enter loan data for 30 years, (360 months),
it sometimes over-runs to 361 months. Now I assume this is due
to rounding errors but I haven't been able to "debug" this and
it's driving me nuts. Can anyone give me some ideas without me
posting the source code? TIA.

BTW: I don't have 2.1f anymore. I lost it after I found out
that windows, by default, doesn't backup .EXE files.


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