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Handling loan repayment in GnuCash::Scheduled Transactions
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The original email thread at http://lists.gnucash.org/pipermail/gnucash-devel/2002-July/006438.html.

July, 2002 - jsled.nosp@m.@asy.nosp@m.nchro.nosp@m.nous.nosp@m..org

API: Scheduled/Periodic/Recurring Transactions

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:

Identifiers:
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.

Functions:
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?

Vastly.

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 manually.

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 variables.

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:

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 provided. 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 created. 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?

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 structures:

/section loansquestions Questions

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. :)

Reference

Other software:

Gnumeric supports the following functions WRT payment calculation:

/section loanspayment Day Two:

As per warlord's comments, the definition of IPMT needs to be updated to account for principal pre-payment. IPMT is actually defined by computation of the value of an account at a specified point in time. This is significant if the loan repayments involve interest.

In the face of creating multiple scheduled transactions for a time range, it may be the case that the relevant account balance is not actually posted to the account at the time of the variable binding. If we intend to show the user an estimation of the IPMT cell value during variable binding, then we would need to do something creative about this ... but as it stands, we'll leave this as an Excercise for the Reader. :)

Druid thoughts...

Page Order:

Intro ->

Params ->

Opts ->

Repayment ->

[Insurance ->]

[PMI ->]

[Taxes ->]

Review/Approval

Intro

"This is a step-by-step method of creating a loan repayment setup within GnuCash. In this Druid, you can input the parameters of your loan and it's repayment and give the details of it's payback. Using that information, the appropriate Scheduled Transactions will be created.

"If you make a mistake or want to make changes later, you can edit the created Scheduled Transactions directly."

Params

Principal        : [amount entry]
Actual Principal : [[optional] amount entry]
Interest Rate    : [numeric entry] %
    Type     : [ ] Fixed
                   [ ] Variable ---------+
                   | Type  : 10/1,7/1,...|
                   | When  : [freqspec?] |
                   +---------------------+
Start Date       : [Gnome Date Entry]
Length           : [num entry] [years|v]
   Remaining     : [num entry]

Options

Do you...
  [ ] ... utilize an escrow account?
      Account: [ acct select |v]
  [ ] ... pay PMI?
      [ ] Via the Escrow account?
  [ ] ... pay insurance?
      [ ] Via the Escrow account?
  [ ] ... pay taxes?
      [ ] Via the Escrow account?
  [ ] ... have some other expense not listed above?
      [ ] Via the Escrow account?

Repayment

Amount        : [ amount entry ]
Assets from   : [ account sel |v] 
Princiapl to  : [ account sel |v]
Interest to   : [ account sel |v]
Escrow to     : [ account sel |v]
Remainder to  : [{escrow,principal,interest}|v]
Frequency     : +- freqspec ----------------+
                |           ....            |
                +---------------------------+

Insurance

Amount : [ amount entry ] Account : [ account sel |v] Frequency : [ ] Part of Repayment Transaction [ ] Other: +- freqspec -------------—+ | .... | +------------------------—+

Taxes/PMI/Other

[ same as Insurance ]

Options in repayment:

http://www.interest.com/hugh/calc/mort_links.html

Druid Feedback:

<Wilddev> jsled: <auspex> Wilddev: The labels need colons, mnemonics, and right-alignment. 
<Wilddev> <auspex> Wilddev: It may be worthwhile for gnucash to create GtkSpinButton subclasses which show the percent symbol and others within the field.
<Wilddev> <auspex> Wilddev: I don't know how complicated that will be.
<Wilddev> <Wilddev> me either :P
<Wilddev> <auspex> Wilddev: The strings need review, but there may be other changes to make first.
<Wilddev> <auspex> Wilddev: "Interest Rate Change Frequency" should perhaps be on the next page?
<Wilddev> jsled: I dont know if you did another page for this, but shouldn't there be a field for ballon amount too?
<jsled> Excellent feedback; thanks.  I don't presently handle baloon payments; how do they work?
<Wilddev> I think, from what I've read before, the are an amount you pay at the end of the loan to close it
<jsled> gnc-account-sel == combo box account selection with pull-down account list [like the register] and auto-completion [hopefully]

<Wilddev> <auspex> Is "Length" the length of a period, or the sum of the periods?
<jsled> The sum of all periods; the length of the loan.
<Wilddev> he's suggesting to think of a better label for that
<Wilddev> ah I thought it was the period between loan transactions
<jsled> Hmm.  Okay.  The between-transaction period is a frequency editor on the Repayment page.
<Wilddev> <auspex> I'm wondering if "Original Principal" should be a vulgate
such as "Loan Amount"

Expression changes, round 2

We need the following abilities in order to get mortgage/loan repayment working:

As well, it'd be nice to have:

We decide that the original/present value of the account should be handled in scheme, and thus we actually need a way to reference accounts down to the scheme expressions. We decide to use the Quote symbols to refer to a string literal. The expression parser should be modified to parse this.

The current 'i' and 'N' are going to be handled by having a list of predefined variables which the user cannot have access to. For the time being, this is 'i' and 'N'.