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Pay the smallest balance or highest rate first?

The smallest-balance method can produce an earlier first payoff. The highest-rate method may reduce modeled interest. Compare both with the same budget, and protect essential bills first.

Pay the smallest balance or highest rate first?
What you are comparingIn this illustration
Same starting balance and period budget60 and 30 illustrative units
Smallest-balance-first modeled interest2.41 units
Highest-rate-first modeled interest2.06 units
Tradeoff shownThe smallest-first path closes its first account sooner in this model.

Choose which result you value

Both schedules start with the same modeled debt and budget. Smallest-balance-first closes an account earlier in this toy model, while highest-rate-first produces less total modeled interest: 2.06 rather than 2.41 illustrative units.

The units are not a promise about dollars saved on real accounts. Compare real schedules using the same payment budget and assumptions. Keep essential bills, disputed debts and legal deadlines outside a purely numerical ranking.

This is a saved illustration with stated assumptions, not an offer or prediction for your circumstances. The full calculation and original limitations are in the optional archive.

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Open the complete calculation, tables and source notesOriginal working documents, complete tables and revision history
About this archive

The explanation above is written for readers. These original working documents preserve the evidence trail, including technical language, dated passages and known corrections. They have not all received independent professional review. Use the marked limits before relying on a particular rule or figure.

Home Data & examples / Two full repayment ledgers: earlier first payoff or lower modeled interest?
DATA & WORKED EXAMPLE

Two full repayment ledgers: earlier first payoff or lower modeled interest?

With the same 60 u starting balance and 30 u period budget, the saved smallest-first path pays 2.41 u interest, while rate-first pays 2.06 u. Smallest-first closes a bucket in period 1; rate-first first closes one in period 2. Both finish in period 3.

Saved research, explicit assumptions and source limits. Full investigation → · All original tables →

6.2 Complete stipulated assumptions — C056

AssumptionStipulation
BucketsAbstract buckets A and B only. No party, account or creditor is represented.
Unitsu, an abstract monetary unit. Computations are rounded to 0.01 u.
Initial balancesA = 20.00 u; B = 40.00 u. Total = 60.00 u.
RatesA = 0.01 per period; B = 0.03 per period, constant throughout. These are not annual rates.
Available payment budget30.00 u per period, stipulated to be available for these two buckets. Actual affordability is not inferred.
Other needsHousing, living expenses, reserves, legal consequences and all other obligations are outside the calculation. Their adequacy is not proved.
Interest conventionAt each period’s start, interest equals the opening balance multiplied by that bucket’s rate. Interest is added before any payment.
RoundingEach bucket’s interest is rounded separately to the nearest 0.01 u, with halves rounded upward. Rounded balances carry forward.
Model minimumFor each bucket, the minimum is the lesser of 5.00 u or its entire balance after that period’s interest. This is an artificial model rule.
Payment orderingFirst satisfy both model minimums. Then allocate the remaining period budget according to the selected strategy.
Smallest-first orderingRank remaining positive balances after minimums, smallest first. No unresolved tie occurs here.
Rate-first orderingTarget B while it remains positive because its rate is higher; then target A.
Payoff and reallocationCap each payment at the remaining balance. Reallocate unused extra immediately within the same period. A paid-off bucket accrues no later interest.
Freed paymentKeep the total available budget at 30.00 u until both buckets are paid. Do not reduce it when one bucket closes.
Final periodPay only the amount needed to reach zero. Record unused budget; do not invent another debt or use for it.
Excluded mechanicsNo fees, new borrowing, rate changes, promotions, penalties, payment delays, grace periods, balance segments, tax effects or external cash flows.

6.3 R032-P1-M001 — Smallest-balance-first

PeriodOpening balancesRaw interest → rounded interestAfter interestModel minimumsAfter minimumsExtra-payment sequenceClosing balancesTotal paid
1(20.00, 40.00)A: 0.2000 → 0.20; B: 1.2000 → 1.20(20.20, 41.20)(5.00, 5.00)(15.20, 36.20)20.00 available: A receives 15.20; remaining 4.80 goes to B(0.00, 31.40)30.00
2(0.00, 31.40)A: 0 → 0.00; B: 0.9420 → 0.94(0.00, 32.34)(0.00, 5.00)(0.00, 27.34)25.00 available: all to B(0.00, 2.34)30.00
3(0.00, 2.34)A: 0 → 0.00; B: 0.0702 → 0.07(0.00, 2.41)(0.00, 2.41)(0.00, 0.00)No extra needed; 27.59 remains unused(0.00, 0.00)2.41

6.4 R032-P1-M002 — Highest-interest-first

PeriodOpening balancesRaw interest → rounded interestAfter interestModel minimumsAfter minimumsExtra-payment sequenceClosing balancesTotal paid
1(20.00, 40.00)A: 0.2000 → 0.20; B: 1.2000 → 1.20(20.20, 41.20)(5.00, 5.00)(15.20, 36.20)20.00 available: all to B(15.20, 16.20)30.00
2(15.20, 16.20)A: 0.1520 → 0.15; B: 0.4860 → 0.49(15.35, 16.69)(5.00, 5.00)(10.35, 11.69)20.00 available: B receives 11.69; remaining 8.31 goes to A(2.04, 0.00)30.00
3(2.04, 0.00)A: 0.0204 → 0.02; B: 0 → 0.00(2.06, 0.00)(2.06, 0.00)(0.00, 0.00)No extra needed; 27.94 remains unused(0.00, 0.00)2.06

6.5 R032-P1-M003 — Conditional comparison

MetricSmallest-firstHighest-rate-firstPermissible conclusion
Total interest2.41 u2.06 uHighest-rate-first costs 0.35 u less in this model.
Total payments62.41 u62.06 uDifference equals the interest difference because initial principal and all other modeled costs match.
First bucket closedPeriod 1Period 2Smallest-first achieves the earlier first closure here.
All buckets closedPeriod 3Period 3This example does not show a difference in the final payoff period.
Unused final-period budget27.59 u27.94 uNeither amount is assigned an actual use.
Motivation or adherenceNot modeledNot modeledNo behavioral conclusion follows.

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What to keep attached

  • These are abstract units and per-period rates, not dollars, annual rates or a household forecast. All 16 saved assumptions must accompany the six complete period rows.
  • Rate-first costs 0.35 u less only within this construction. Motivation, adherence, essential-needs adequacy, contractual allocation and real savings are not established.
  • P2 replaces only fragmented formula presentation; it changes no input, ledger row or result.

Source trail

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