loan/mortgage repayment via sched xactions: feedback request

Josh Sled
Tue, 2 Jul 2002 21:52:10 -0700

The following is something I wrote up today while coming to grips with
Loan/Mortgage [re-]payment, and how it could function w/in GnuCash and
Scheduled Transactions.

I deliniate a course of feedback which I will follow near the end, but
would appreciate your feedback.


Handling loan repayment in GnuCash::Scheduled Transactions
2002.07.02 -

Bugs 84892 and 84877 detail a request for a new Loan/Mortgage account type,
and Scheduled Transaction support for loan repayment.  While it's debatable
that a new account type is required, there is definitely a need for Scheduled
Transaction support for interest/payment computation for a parameterized
"loan repayment SX".

The nature of this support will not create a new top-level account type, but
instead will result in the following changes:
 a. Support in the SX credit/debit formulas for such calculations.
 b. A Druid to assist in the creation of such SXes.
 [c. budgeting/tool bench support in the future]

We define loan repayment values in the following terms:

P  : the original principal.  This is the overall principal afforded by the
     loan at the time of it's creation.
P' : The beginning principal.  This is the principal at the time of entry
     into GnuCash.
I :  The interest rate associated with the loan.  Note that this may change
     over time [based on an addition to the Prime rate, for instance], at
     various frequencies [yearly, monthly, quarterly...].  Ideally, we can
     use the FreqSpec mechanism to facilitate the interest rate adjustment.
N  : The length of the loan in periods.
m  : The minimum periodic payment.
n  : The current period of the repayment.

PMT  : Total equal periodic payment, as per Gnumeric/Excel's definitions
       [see end for more detail].
IPMT : Monthly payment interest portion,  ""
PPMT : Monthly payment principal portion, ""

[ NOTE: 'PMT(I,N,P) = IPMT(I, n, N, P) + PPMT(I, n, N, P)' for 0 <= n < N ]

The formula entered into the SX template for a loan may then look like:

Example 1:
Desc/Memo |                     Account |         Credit |           Debit
Repayment | Assets:Bank:Checking        |                | =PMT(I,n,N,P)
          |                             |                |  + fixed_amt
Interest  | Expenses:Loan_Name:Interest | =IPMT(I,n,N,P) |
PMI       | Expenses:Loan_Name:Misc     | fixed_amt      |
Principal | Liabilities:Loan_Name       | =PPMT(I,n,N,P) |

Or, in the case where an escrow account is involved [with thanks to warlord
for the review and fixes]:

Example 2:
Desc/Memo      |             Account         |       Credit   |       Debit
Repayment      | Assets:Bank:Checking        |                | =PMT(I,n,N,P)
               |                             |                | + escrow_amt
               |                             |                | + fixed_amt
               |                             |                | + pre_payment
Escrow         | Assets:Loan_Escrow_acct     | escrow_amt     |
Interest       | Expenses:Loan_Name:Interest | =IPMT(I,n,N,P) |
PMI            | Expenses:Loan_Name:Misc     | fixed_amt      |
Principal      | Liabilities:Loan_Name       | =PPMT(I,n,N,P) |
               |                             | + pre_payment  |
FreqSpec = 1 month

Desc/Memo      |             Account         |       Credit   |       Debit
Insurance      | Assets:Loan_Escrow_acct     |                | insurance_amt
Insurance      | Expenses:Home_Insurance     | insurance_amt  |
FreqSpec = 1 year

Desc/Memo      |             Account         |       Credit   |       Debit
Taxes          | Assets:Loan_Escrow_acct     |                | taxes_amt
Taxes          | Expenses:Property_Taxes     | taxes_amt      |
FreqSpec = Quarterly


Practical questions regarding the implementation of this facility are:

| 1. The transactions as in Example 2 are not going to be scheduled for the
|    same day; are their values linked at all / do they need to share the
|    same var bindings?

Yes, they would want to be linked.  More precisely, the insurance/tax amounts
are very likely linked to the escrow_amt in Ex.2.  Unfortunately, these are
very likely separate SXes...

| 2. How does this effect the SX implementation of variables?


It becomes clear that multiple SXes will be related.  While they'll have
separate FreqSpecs and template transactions, they'll share some state.  For
both visualization [i.e., the SX list] and processing [credit/debit cell
value computation] we'll want some manner of dealing with this.

It becomes clear as well that the nature of variables and functions needs to
be more clearly defined with respect to these issues.  We probably want to
institute a clear policy for the scoping of variables.  As well, since the
SXes will have different instantiation dates, we'll need a method and
implementation for the relation of SXes to each other.

A substantial hurdle is that if a set of SXes are [strongly] related, there
is no-longer a single instantiation date for a set of related SXes.  In fact,
there may be different frequencies of recurrence.

One option -- on the surface -- to relate them would be to maintain an
instance variable-binding frame cache, which would store user-entered and
computed variable bindings.  The first instantiated SX of the set would create
the frame, and the "last" instance would clean it up.  First "last" instance
is defined by the last-occurring SX in a related set, in a given time range.

For example: a loan SX-set is defined by two monthly SXes ["repayment" and
"insurance"], and a quarterly "tax" SX.  The first monthly SX would create a
frame, which would be passed two the second monthly SX.  This would occur for
the 3 months of interest.  The Quarterly SX would get all 3 frames for it's
creation, and use them in an /appropriate/ [read: to be defined through a lot
of pain] way.  As the time-based dependency relationship between the frames
plays out, the frame can be removed from the system.

Another option is to toss this idea entirely and instead let the user DTRT

A related option is to add the necessary grouping mechanism to the SX
storage/data structure: immediately allowing visual grouping of related SXes,
and potentially allowing a storage place for such frame data in the future
with less file-versioning headache.  This is the option that will be pursued.

Another element implicit in the original requirements to support
loans/repayment calculations is implicit variables.  These are symbolic names
which can be used and are automagically bound to values.  The known implicit
variables to support loan/repayment are:

P [loan principal amount], N [loan repayment periods], I [interest], m
[minimum payment] and n [current period].  Some of these [P, N, I, m] are
fixed over many instances; some [n] are rebound specific to the instance.
See the 'variable-scope-frame' below for a method of handling these

And yet-another element implicit in the original requirement is support for
detecting and computing the result of functions in the template transaction's
credit/debit cells.  Changes to the src/app-utils/gnc-exp-parser.[hc] and
src/calculation/expression_parser.[ch] to support functions would be
necessitated.  It is conceivable that after parsing, the parsed expression
could be passed to scheme for evaluation.  Hopefully this would make it
easier to add support for new functions to the SX code via Scheme.

| 3. How do we deal with periodic [yearly, semi-yearly] updating of various
|    "fixed" variables?

Another change in the way variables are used is that some SXes -- especially
loan-repayment -- may involve variables which are not tied to the instance of
the SX, but rather to variables which:
. are also involved in another SX
. change with a frequency different than the SX
. are represented by a relationship to the outside world ["prime + 1.7"]

A partial fix for this problem is to provide multiple levels of scope for
variable bindings, and expose this to the user by a method of assigning
[perhaps time-dependent] values to these variables.  Variables bound in this
manner would absolve the user of the need to bind them at SX-creation time.

An added benefit of this would be to allow some users [see Bug#85707] have
"fixed variable" values for a group of SXes.

In combination with the SX Grouping, this would provide most of a fix for the
problem described in #2, above.  The variable_frame could be used to provide
the shared-state between related SXes, without imposing quite the same
burden.  This approach is slightly less flexible, but that allows it to be
implemented more readily, and understood more easily.

A question which comes up when thinking about yearly-changing values such as
interest rates is if the historical information needs to be versioned.  For
now, we punt on this issue, but hopefully will provide enough of a framework
for this to be reasonably added in the future.

We define four types of variables supported by this scheme:

implicit  : provided only by the system
            e.g.: 'n', the current index of the repayment

transient : have user-defined values, bound at instantiation time.
            e.g.: existing ad-hoc variables in SXes.

static    : have a user-defined values, and are not expected to change with
            any measurable frequency.  The user may change these at their
            leisure, but no facility to assist or encourage this is
            e.g.: paycheck amount, loan principal amount 

periodic  : have user-defined values which change at specific points in
            time [July 1, yearly].  After the expiration of a variable value,
            it's re-binding will prevent any dependent SXes from being
            e.g.: loan tax amount, loan interest rate

| 4. From where do we get the dollar amount against which to do the [PI]PMT
|    calculation?

The user will specify the parameters of the Loan via some UI... then where
does the data go?

. KVP data for that account?
. KVP data for the SX?
. Do we have a different top-level "Loan" object?
. Present only in the SX template transactions/variable-frames?

I believe that the only location of the data after Druid creation is in the
variable-binding frames and the formulae in the template transactions.  The
Druid would thus simply assist the user in creating the following SX-related

. SXGroup: Loan Repayment
  . variable_frame
    . P [static]
    . N [static]
    . n [implicit]
    . I [periodic]
    . pmi_amount [periodic]
    . tax_amount [periodic]
    . pre_payment [periodic]
    . insurance_amount [periodic]
  . SX: Payment
    . Bank -> { Escrow,
                Expense:Loan:Insurance }
  . SX: Tax
    . Escrow -> Expense:Tax
  . SX: Insurance
    . Escrow -> Expense:Insurance



1/ UI - visible should all this machination be to the user?  Should they even
   see them as such.  The current SX since-last-run UI makes them pretty
   visible, and in my estimation it actually helps to make them a bit more
   formal and visible.  At the same time, it may be overwhelming for the user
   to have to create formal variables with weird types like "implicit",
   "transient", "static", and "periodic".


Priorities, Plan

The above represents an "ideal" set of extensions to the SX framework to
enable multiple "enhancement"-level functionalities.  Therefore, the
following is the prioritized schedule, with annotations:

1. Functions [PMT, [IP]PMT] in exp_parser; implicit variables [n].
2. [Visual-only] SX grouping
3. Loan-repayment creation Druid
4. SX-only static vars
5. SX-only periodic vars
6. SX-group vars, var_frames

After the completion of item 4, the feature can safely be called "finished".
Items 5 and 6 only serve to increase the robustness of the facility and make
the user's life slightly easier, at the cost of making _my_ life harder. :)



Other software:

Gnumeric supports the following functions WRT payment calculation:

* PMT( rate, nper, pv [, fv, type] )
  PMT returns the amount of payment for a loan based on a constant interest
  rate and constant payments (ea. payment equal).
  @rate : constant interest rate
  @nper : overall number of payments
  @pv   : present value
  @fv   : future value
  @type : payment type
          . 0 : end of period
          . 1 : beginning of period

* IPMT( rate, per, nper, pv, fv, type )
  IPMT calculates the amount of a payment of an annuity going towards
  interest. Formula for IPMT is:
  IPMT(per) = - principal(per-1) * interest_rate
  principal(per-1) = amount of the remaining principal from last period.

* ISPMT( rate, per, nper, pv )
  ISPMT returns the interest paid on a given period.
  If @per < 1 or @per > @nper, returns #NUM! err.

* PPMT(rate, per, nper, pv [, fv, type] )
  PPMT calculates the amount of a payment of an annuity going towards
  PPMT(per) = PMT - IPMT(per)
  where: PMT is payment
         IPMT is interest for period per

* PV( rate, nper, pmt [, fv, type] )
  Calculates the present value of an investment
  @rate : periodic interest rate
  @nper : number of compounding periods
  @pmt  : payment made each period
  @fv   : future value