Where your loan payment goes: interest, fees, and principal

SettleADebt R004 PASS-03

Federal closed-end prepayment, unearned-interest refunds, and sum-of-digits/actuarial comparisons

The federal refund duty, the restriction on the refund method, and the duty to disclose prepayment terms are separate rules. Under the text read, 15 U.S.C. §1615(a) requires a prompt refund of unearned interest when its full-prepayment trigger is met, subject to its less-than-$1 exception. Section 1615(b) imposes an additional actuarial-method floor for specified precomputed transactions exceeding 61 months and consummated after September 30, 1993. That threshold is not a general permission to use Rule of 78s on shorter transactions, and neither provision establishes a universal right to make a partial principal payment. uscode.house.gov

Regulation Z’s prepayment disclosures identify whether a penalty or rebate applies under the relevant branch. They do not themselves establish that a charge is lawful, supply a complete payoff calculation, or determine every consequence of an extra payment. The applicable legal obligation and other applicable law remain necessary. ecfr.gov+2

Actual research date: October 27, 2026, America/Los_Angeles. Clock observations bracketed this pass from 2:26:28 p.m. through 2:36:14 p.m. PDT—21:26:28 through 21:36:14 UTC. Source-check dates below refer to that date, not to a document’s effective date.

Foundation and result status

1. Source table

All IDs below have the prefix R004-P3-. Related representations of the same statute or regulation are grouped or expressly identified as such; they are not independent corroborating authorities.

“Fresh read” means content actually returned and read during this pass. PDF text extraction is identified separately from pixel inspection. No PDF/image pixel inspection is claimed in P03.

2. Atomic claim table: federal statutory triggers

Area A004 applies to every claim in this report. “Established” below means supported at the stated general level and within the source/version bounds; it does not mean an actual transaction satisfies the predicates.

A detail preserved from the literal read: §1615(d)(2)’s heading refers to “Consumer, credit,” while its operative sentence imports consumer and creditor. This report follows the operative sentence and subsection (d)(3); it does not silently rewrite the statute. uscode.house.gov

What the 61-month rule does—and does not—decide

A stipulated 62-month precomputed transaction consummated October1,1993 passes the term/date portion of §1615(b). A 61-month transaction does not. A 62-month transaction consummated September30,1993 does not satisfy “after” that date. These comparisons do not decide the other predicates, any more protective law, or whether a particular prepayment is contractually permitted.

Likewise, the relevant term cannot simply be replaced with the number of payments remaining when an early payment is contemplated. A modification, refinancing, or disputed consummation date requires its own legal characterization. The report does not resolve historical application merely because the current compiled section lacks an additional date limitation in (a) or (c). C009–C010; S001.

3. Atomic claim table: disclosures, classifications, and contract control

The statutory disclosure foundation is §1638(a)(11), with a contract-reference requirement in (a)(12). Regulation Z then supplies the operative disclosure branches and commentary. uscode.house.gov

Necessary product boundary

The general §18 scope commentary routes ordinary real-property/cooperative-unit transactions subject to §19(e)/(f) to the integrated mortgage disclosures, while retaining specified personal-property and reverse-mortgage branches under §18. Section3(h) creates a narrow alternative for qualifying assistance transactions.

For that alternative, the conditions actually read include a subordinate lien; a listed housing-assistance purpose; no contractual interest; specified forgiveness or deferral—including the stated 20-year, sale, or principal-residence alternatives; restricted closing costs; the stated application/counseling-fee condition; and compliant disclosures. These conditions are recorded to prevent a false “all mortgages are excluded from §18” inference. Their application and all substantive mortgage prepayment restrictions remain held. C020, C035; S006, S008. Consumer Financial Protection Bureau+1

4. What the allocation methods actually calculate

Sum of digits

For the equal-period, equal-installment model used below:

Plain text

n = original number of stipulated monthly installments
k = number of full model periods elapsed, with scheduled installments paid
F = total precomputed interest charge
S(n) = 1 + 2 + ... + n = n * (n + 1) / 2

Period-j allocated interest = F * (n - j + 1) / S(n)

Unearned amount after period k:
R_digits(k) = F * S(n - k) / S(n)

Allocated earned amount:
E_digits(k) = F - R_digits(k)

The familiar denominator is 78 only when n = 12. For three installments it is 6; for six it is 21. The official Wisconsin explanation uses descending installment weights and expressly discusses terms other than twelve months. The generalized notation above is a mathematical restatement of that construction. dfi.wi.gov

This calculation allocates a specified precomputed charge. It does not establish the charge’s legality, identify the correct contractual refund method, determine whether payment was received on time, or say that every extra remittance changes k. In this illustration, elapsed periods and paid scheduled installments coincide. Irregular timing, unequal payments, extensions, and partial prepayments require further rules.

Constant-rate balance allocation

The Federal Reserve’s generic constant-yield explanation allocates interest using outstanding principal times a periodic rate, with the remainder of a payment credited to principal. Its example expressly warns that law, contracts, and implementations may differ. federalreserve.gov+1

For this pass’s stipulated model:

Plain text

I_k = r * B_(k-1)
principal_component_k = C_k - I_k
B_k = B_(k-1) + I_k - C_k

G_k = sum of remaining scheduled payments
R_balance(k) = G_k - B_k

Here:

• B_k is a model net balance used for the comparison.
• G_k is the remaining gross precomputed obligation.
• r is a stipulated rate per model month.
• The refund comparison is made immediately after an on-time installment, with no additional elapsed fraction.

This is an actuarial-style mathematical benchmark, consistent with the read payment-allocation concept. It is not a determination of the legally required §1615 refund. The statute’s definition has been read completely, but no actual contract, applicable refund rate, timing convention, state definition, or complete transaction-specific method has been established. The definition’s deficiency language also does not authorize real-world capitalization.

5. Eight worked branches

There are eight branches: four new arithmetic branches—W02, W03, W04, W06—one reviewed numerical reuse, W01, and three qualitative/trigger branches, W05, W07, W08. W03 compares two allocation rules for one new stipulated set of cash flows. It does not rerun a P01 schedule.

W03: fully specified new arithmetic illustration

The 10% monthly factor is deliberately artificial to produce transparent exact-dollar arithmetic. It is not a live quote, lawful-rate finding, annual note rate, disclosed APR, or effective annual yield.

Balance-method steps

After installment1:

Plain text

Remaining gross scheduled payments = 133.10 + 133.10 = 266.20
Balance-method unearned amount = 266.20 - 231.00 = 35.20
Net prepayment benchmark = 266.20 - 35.20 = 231.00

Sum-of-digits denominator = 3 + 2 + 1 = 6
Sum-of-digits unearned amount = 68.30 * (2 + 1) / 6 = 34.15
Net prepayment under that model = 266.20 - 34.15 = 232.05

The difference is $1.05. Under these inputs, the sum-of-digits allocation retains more interest at that point. This is not a universal numerical relationship for every possible transaction.

Reconciliation at the two hypothetical payoff points

For the second sum-of-digits point:

Plain text

Unrounded unearned amount = 68.30 / 6 = 11.383333...
Cash-rounded unearned amount = 11.38
Net prepayment = 133.10 - 11.38 = 121.72
Total net cash = 266.20 + 121.72 = 387.92
Retained charge = 387.92 - 331.00 = 56.92

The cent adjustment is disclosed; the report does not pretend that the fractional-cent ledger amount and cash refund are identical.

Cash conservation at the first payoff point is:

Plain text

Balance benchmark:
133.10 + 231.00 = 331.00 + 33.10 = 364.10

Sum of digits:
133.10 + 232.05 = 331.00 + 34.15 = 365.15

If the remaining gross amount were paid first and the refund returned separately, the nominal net cash would instead be:

Plain text

prior cash + gross prepayment - refund

If the refund is deducted in calculating the payment, it is:

Plain text

prior cash + (gross prepayment - refund)

The refund appears once in either accounting route. A later cash refund can have different timing consequences from an immediate deduction; nominal equality does not certify equal present value or lawful delivery timing. The Federal Reserve’s generic explanation describes both refund and deduction structures, subject to its limitations. federalreserve.gov

Explicit arithmetic self-check ledger

These are 32 explicitly listed arithmetic checks, not 32 independent reviews, software tests, or compliance validations. Checks01–31 concern the new hypothetical branches; check32 identifies the source inconsistency. W01’s reviewed schedules were not recalculated.

6. Reconciliation and blank generic prepayment audit worksheet

Two different starting balances must not be mixed.

Accruing-balance route:

Plain text

Conditional payoff =
  outstanding principal
+ accrued, unpaid earned interest through the applicable endpoint
+ separately authorized amounts not already included
- applicable credits/refunds not already applied

Gross precomputed-obligation route:

Plain text

Remaining gross obligation =
  original scheduled gross obligation
- payments already credited against that obligation
- adjustments already credited

Conditional net prepayment =
  remaining gross obligation
- applicable unearned-charge refund
- other unapplied credits
+ separately authorized penalty
+ any lawful incremental minimum-charge adjustment
+ other authorized amounts not already included

These are reconciliation structures, not legal payoff formulas valid for every debt. Prior payments must not be subtracted again from an already-net principal balance. Future unearned interest must not be subtracted from a balance that never included it. A refund already netted into a payoff must not also be counted as a second cash receipt.

For a fee-free precomputed model, the check is:

Plain text

prior payments + net prepayment = original principal + retained earned interest

Other charges, credits, and separate cash flows must be added explicitly if they exist and are legally applicable.

Blank worksheet

This worksheet is intentionally generic. It contains no person, creditor, account, property, license, or case identifier and is not a request to obtain records.

A future generic packet can examine published state/product law and blank-form clauses. Under the present owner limits, that research still cannot prove what a particular consumer agreed to or determine an actual payoff.

7. Atomic claim table: mathematics, reconciliation, and evidence limits

8. Granular coverage table

“Answered” refers to the stated generic research question. It does not mean actual application has been resolved.

9. Question-to-source/claim crosswalk

10. Source-read and failure log

All actions occurred October27,2026 PDT. Search snippets, navigation pages, and search-only discoveries were not treated as complete operative reads.

11. Self-check and remaining holds

Researcher self-check—not independent review

Precise remaining packets and boundaries

The supported result of this pass is a federal trigger and disclosure framework plus transparent conditional arithmetic. The reviewed $170.57 simple-interest saving remains intact. The new comparison shows how two specified allocations can produce different retained-interest and net-payment amounts from the same original scheduled cash flows. Neither result determines an actual lawful charge or refund.

END R004 PASS-03.