GnuCash  5.6-150-g038405b370+
Handling loan repayment in GnuCash::Scheduled Transactions
The original email thread at https://lists.gnucash.org/pipermail/gnucash-devel/2002-July/006438.html.

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:

• 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 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?

• 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 structures:

• 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, Liability:Loan:Principal, Expense:Loan:Interest, Expense:Loan:Insurance }
• SX: Tax
• Escrow -> Expense:Tax
• SX: Insurance
• Escrow -> Expense:Insurance

# Reference

## 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). : constant interest rate : overall number of payments : present value : future value : 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 where: 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 < 1 or > , returns #NUM! err.
• PPMT(rate, per, nper, pv [, fv, type] ) PPMT calculates the amount of a payment of an annuity going towards principal. 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 : periodic interest rate : number of compounding periods : payment made each period : future value