# Amortization Formuli

``` BBS: Inland Empire Archive
Date: 07-11-92 (16:02)             Number: 287
From: DON KROUSE                   Refer#: NONE
To: RICHARD ATTENBOROUGH          Recvd: NO
Subj: Amortization Formuli           Conf: (2) Quik_Bas```
```PL> RA> basis. Maybe I am just missaplying the equation. It seems to tell me
PL> RA> that if I go from monthly payments to biweekly payments that I end up
PL> RA> paying the same amount of money! (wierd) Here is the equation that I
PL> RA> have.
Hi Richard,
I missed your original post, but saw part of your message that someone
else quoted. I've been a loan officer for many years, and have written
quite a few applications that involve "Time Value of Money" calculations,
so mabey I can help. The problem is not in the use of the formula, it's
in an incorrect assumption of what a BiWeekly mortgage is. A BiWeekly
mortgage is simply a monthly mortgage in which you pay half of the monthly
payment amount every two weeks. This amounts to the eqiuvalent of 13
monthly payments per year instead of 12. There is only a small effect
from increasing the number of Payment/Interest periods. The big effect is
from accelerated principal reduction. The excess payments reduce the
principal balance which therefore reduces the interest due for the next
period which means that even more of the next payment goes to reduce
principal......... The end effect is that a 30 year loan will pay off in
"about" 20 years. It varies a little depending on the interest rate. You
pay about 1/12 more per year, but you pay for about a third less years.
Below is a small pgm that illustrates the principle. It is not well
commented, to save space, so if it's not clear just ask. The _ at the end
of some lines means that it is continued on the next line. MAKE SURE YOU
APPEND THEM!
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Calc:
CLS
INPUT "Annual Interest Rate "; I#
INPUT "Loan Amount "; PV#
PPY% = 12
FV# = 0
N# = 360
MonthI# = I# / 1200
BiWeekI# = I# / 2600
WeekI# = I# / 5200
'---- Calc payment amount
MonthPmt# = -PV# / ((1 - (1 + MonthI#) ^ -N#) / MonthI#)
BiWeekPmt# = MonthPmt# / 2
WeekPmt# = MonthPmt# / 4
'---- Calc no. of patments necessary to amortize
MonthN# = -(LOG(1 - ((MonthI# * PV#) / -MonthPmt#)) / LOG(1 + MonthI#)) +-
(LOG(1 - ((MonthI# * -FV#) / -MonthPmt#)) / LOG(1 + MonthI#))
BiWeekN# = -(LOG(1 - ((BiWeekI# * PV#) / -BiWeekPmt#)) / LOG(1 + BiWeekI#)_
) + (LOG(1 - ((BiWeekI# * -FV#) / -BiWeekPmt#)) / LOG(1 + BiWeekI#))
WeekN# = -(LOG(1 - ((WeekI# * PV#) / -WeekPmt#)) / LOG(1 + WeekI#)) + (LOG_
(1 - ((WeekI# * -FV#) / -WeekPmt#)) / LOG(1 + WeekI#))
'---- Convert the no. of payments to years
MonthYrs# = MonthN# / 12
BiWeekYrs# = BiWeekN# / 26
WeekYrs# = WeekN# / 52
'---- Calc the total amount paid
TotalMonthPaid# = MonthN# * MonthPmt#
TotalBiWeekPaid# = BiWeekN# * BiWeekPmt#
TotalWeekPaid# = WeekN# * WeekPmt#
'---- Calc the total interest paid
MonthInterestPaid# = TotalMonthPaid# + PV#
BiWeekInterestPaid# = TotalBiWeekPaid# + PV#
WeekInterestPaid# = TotalWeekPaid# + PV#
'---- Print to screen
PRINT "                        Monthly        BiWeekly       Weekly"
PRINT "                     -------------   ------------  ------------"
PRINT USING "Payment                  #####,.##      #####,.##     #####,_
.##"; MonthPmt#; BiWeekPmt#; WeekPmt#
PRINT USING "No. payments              ####,          ####,         ####,"_
; MonthN#; BiWeekN#; WeekN#
PRINT USING "Number of years           ####,.##       ####,.##      ####,._
##"; MonthYrs#; BiWeekYrs#; WeekYrs#
PRINT USING "Apx Total Payments    ########,.##   ########,.##  ########,._
##"; ABS(TotalMonthPaid#); ABS(TotalBiWeekPaid#); ABS(TotalWeekPaid#)
PRINT USING "Apx Total Interest    ########,.##   ########,.##  ########,._
##"; MonthInterestPaid#; BiWeekInterestPaid#; WeekInterestPaid#
PRINT:PRINT "Press ESC to QUIT or any other key to calculate another term"
DO
ky\$ = INKEY\$
LOOP WHILE ky\$ = ""
SELECT CASE ky\$
CASE CHR\$(27):END
CASE ELSE:GOTO Calc
END SELECT
' That's ALL
--- FMail 0.90
* Origin: Silver Lake Systems * Bothell,WA (1:343/58)
```

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