[GNC] Loan/Mortgage payments with "adjusted" principle (eg after an extra principle payment), SOLVED

[Mike or Penny Novack]

On 8/12/2018 12:58 PM, azalea4va wrote:
> Sorry, I missed this reply.  So a little late, but ...
I should perhaps have indicated that writing this sort of thing used to 
be "my line of country". I have written these things.
> Mike or Penny Novack-3 wrote
>> a) method? << by "present value" of series of "rents" or by "trial and
>> error" >>
> I am not sure what ""present value" of series of "rents"" means, but the
> answer is by math.  This is just a mathematical calculation.  As was
> indicated in the code provided.  I did not specify, but the math was based
> on 30/360 calculations, the one most often used in determining mortgage
> payments.
OK --- The periodic payments are called "rents" and dependent on the 
"discount rate" (the mortgage interest rate in this case) that series of 
future payments has a PRESENT value. So ONE way of doing the math is to 
take the payment amount to be 1.0000... (number of decimal places not 
going to be agreed) and discounting each by the interest for the 
interval. That gives a number you can divide into the starting principle 
amount.

Another way for a program to address the problem is "trail and 
error"where starting with an initial guess as to what the payment would 
be this is adjusted until the "best fit" results << see my question 
about "final payment" >>


> Mike or Penny Novack-3 wrote
>> b) where will rounding take place?
> I addressed this in the file I provided.  There is one and only one correct
> answer mathematically.
Not true. Depends, for example, on how many decimal places in the 
calculations and whether only final rounding or rounding at multiple 
places during the calculations. Since you and the bank will not be in 
agreement won;t get the same answer. Again I will refer to the alternate 
"trial and error" method of calculating the payment which MIGHT give 
better results.
>
>
> Mike or Penny Novack-3 wrote
>> c) how will the final payment be figured?
> To be honest, I forget (because I do not care).  Did I add the code to to
> make the final payment the amount due at that time?
Again, there are choices here. Was the calculation made so that there 
was NO additional (small) payment at the end? Was the calculation such 
that the final payment would be as close as possible but not more than 
the rest of the payments? What do you do IF the choice is between a 
final payment much smaller than the others or going over a small amount 
if the payment amount is 1 cent higher?

Do these issues explain why (in practice) my "amortab" programs (create 
an amortization table for a loan amount, interest rate, and number of 
payments) were usually written to use the "trial and error" method? << I 
might get a first approximation by calculating the "present value" and 
THEN seeing if small adjustments up or down gave a better fit to all the 
desired conditions. >> For understanding what I mean by "trial and 
error" methods look up something like "Newton's Method" -- I was NOT 
referring to "non-math" but an algorithm, a PROCESS,  guaranteed to 
converge on a best approximation of a value.

Michael D Novack