Optimise calculators

Optimisation tools take a multi-variable problem with a clear objective and search for the input combination that produces the best outcome. In personal finance, the most common optimisation problem is debt: given a stack of debts with different rates, balances, and minimums, plus a fixed monthly surplus, what is the allocation that pays everything off fastest or cheapest?

These calculators apply formal optimisation to financial questions that most people answer by intuition or single-strategy heuristics. The debt-payoff optimiser, for example, doesn't pick between snowball and avalanche on principle — it runs both and reports which is better for your specific stack, by how much, and across what horizon. The output is the strategy and the cost of choosing wrong.

All maths uses 20-digit decimal precision. The simulation engines run month-by-month with full amortisation, applying minimums to every debt and the surplus to the priority debt under each strategy. We make no jurisdiction-specific assumptions about loan products, tax shields, or insolvency law — you supply your local numbers.

What is financial optimisation?

A financial optimisation problem has three parts: a set of decision variables (the things you can choose — payment amounts, allocations, timing), a set of constraints (rules you can't break — minimum payments, available cash, contractual terms), and an objective function (the outcome you want to maximise or minimise — usually total interest, time to debt-free, or terminal wealth).

Solving the problem analytically is hard for anything beyond the simplest cases, but simulation works fine for most personal-finance optimisation. The optimiser tries each candidate strategy under the same constraints and reports the one with the best objective. For debt payoff, the candidate strategies are well-known: snowball, avalanche, and various blended approaches.

Worked example: a borrower with three debts — $4,000 on a credit card at 22%, $12,000 on a personal loan at 11%, and $8,000 on a vehicle loan at 7% — has $400/month above minimums to allocate. Avalanche directs the surplus to the 22% card first, then the 11% loan, then the 7% loan. Snowball directs it to the $4,000 card first (smallest balance), then the $8,000 vehicle, then the $12,000 loan. Both strategies pay all three off; the gap between them is the optimisation question.

The value of an optimiser is not just the answer — it is the gap. Knowing that snowball costs $1,200 more than avalanche on your stack but saves you 14 months of small-balance friction is the kind of trade-off that informs a real decision. Without the gap, the choice is just preference; with the gap, it is informed preference.

Debt payoff optimisation

The debt-payoff optimiser takes your full debt stack, your minimum payments, and your monthly surplus, and runs the simulation under each candidate strategy: avalanche (highest rate first), snowball (smallest balance first), and any user-specified ordering. The output for each strategy is total interest paid, months to debt-free, and the per-month payment schedule.

Avalanche is mathematically optimal for total interest, always — it directs every surplus dollar to the debt with the highest marginal cost. But the gap between avalanche and snowball is rarely as large as the maths suggests. On a typical 4-debt stack, avalanche saves a few hundred to a few thousand dollars over a payoff period of 3–5 years. For most borrowers, this gap is small relative to the behavioural advantage of fast wins from snowball.

Worked example: on a $30,000 stack split across two credit cards (18% and 24%), a personal loan (12%), and a vehicle loan (8%), with $500/month above minimums, avalanche typically clears the stack in roughly 51 months and costs about $7,200 in interest. Snowball typically clears in 53–54 months and costs about $7,900 in interest. The avalanche advantage is real but modest — under $700 over four-and-a-half years, or roughly $13/month.

The optimiser also handles edge cases the simple strategies miss. If one debt has a balance just below where the surplus could clear it in a single month, paying that one off first frees up its minimum to roll into the next debt's payment — a subtle compounding that pure avalanche or pure snowball ignore. The debt-payoff-optimiser surfaces these cases and recommends a hybrid ordering when the maths supports one.

How optimisation differs from manual strategy selection

Most borrowers approach debt the same way: pick a strategy on principle (usually whichever sounds most intuitive), apply it consistently, and hope the maths works out. The two most common picks are snowball — backed by behavioural research showing that fast wins increase persistence — and avalanche, backed by anyone who has ever looked at a compound-interest table. Both are reasonable defaults; neither is provably the best strategy for any particular stack without running the numbers.

Manual selection is a single-trial decision: you pick one strategy and live with it. Optimisation is a multi-trial comparison: the engine runs every candidate strategy through the same simulation and reports which finished first, which paid the least interest, and where the curves crossed. The optimiser doesn't argue the case for any one strategy — it just reports the data and lets the gap decide.

The crucial difference is that optimisation removes the guesswork without removing the choice. Once the gap between strategies is small (say, under $500 over a 4-year payoff), the borrower is free to pick the one that fits their psychology. When the gap is large (several thousand dollars or many months), the maths is unambiguous — and the borrower can choose snowball anyway, but they do it with full knowledge of what it costs. That informed choice is what an optimiser produces; pure intuition cannot.

Manual strategy selection also tends to be static — pick a strategy at the start and follow it through. The optimiser supports re-running the simulation whenever the inputs change: a balance transfer, a new debt, a one-off lump sum, an income increase. Each rerun confirms whether the original strategy is still optimal or whether a switch makes more sense given the updated stack. Few borrowers re-optimise; the ones who do typically discover that a small mid-payoff adjustment saves several hundred dollars more.

When extra payments have the most impact

Extra payments are not all created equal. The same $100/month above minimums saves wildly different amounts depending on which debt it targets, when in the payoff cycle it is applied, and how long the underlying loan would otherwise have run. Understanding the diminishing-returns curve is the difference between feeling like extra payments are wasted and seeing them clearly accelerate the timeline.

The first dollar of extra payment per month tends to have the highest marginal impact. On a $30,000 debt stack, the first $100/month of surplus typically removes 10–14 months from the payoff and saves $1,500–$2,500 in interest. The next $100/month removes a further 7–9 months and saves $800–$1,200. The third $100/month removes 4–6 months and saves $500–$700. Each successive $100/month buys less because the remaining stack is smaller and pays off sooner anyway.

The same diminishing-returns shape applies across the payoff timeline. An extra payment applied in month 1 of a 60-month payoff compounds against 59 future months of interest. The same payment in month 30 compounds against only 30 future months. The same payment in month 50 compounds against 10 months. This is why financial planners say "as much as you can, as early as you can" — early extras are worth roughly twice late extras on a typical consumer-debt stack.

The optimiser quantifies this directly. Run the same stack at three surplus levels — $0/month, $100/month, $200/month — and compare the total-interest figure for each. The savings from going $0 → $100 will dwarf the savings from going $100 → $200, and that gap will dwarf the savings from going $200 → $300. The shape of that curve tells you where the next dollar of surplus has its highest return — and where additional surplus would be better deployed elsewhere (an emergency fund, an investment account) once the marginal interest saving falls below your other priorities.

Beyond debt — where optimisation tools are heading

Debt is the most accessible optimisation problem because the constraints are simple and the objective is unambiguous. But the same machinery applies to other personal-finance questions: portfolio rebalancing, tax-loss harvesting, retirement contribution allocation, savings goal sequencing, and emergency-fund-vs-investment trade-offs.

Portfolio optimisation is harder because returns are uncertain and the objective is risk-adjusted rather than absolute. But the simulation method extends naturally: try multiple allocations, run them through a Monte Carlo or scenario engine, and report the allocation that maximises expected utility. Future versions of this pillar will extend the optimiser to portfolio decisions once the data and engines are validated.

Tax-loss harvesting is another optimisation candidate: given a portfolio with embedded gains and losses, what is the trade pattern that maximises after-tax wealth subject to wash-sale and rebalancing constraints? Like debt payoff, the problem can be approached by simulation; unlike debt payoff, the answer is highly jurisdiction-specific and likely best served by a future locale-aware tool.

For now, the debt-payoff optimiser is the only optimisation tool in production. It is, however, the optimisation problem most likely to materially change a household's financial trajectory — which is why it is the one we built first.