Methodology

The math behind
every number.

No black boxes. Every advanced widget in Wealth Prognosis is documented here with its exact formula, inputs and a worked example — so you can trust the output, audit it, and reproduce it.

Jump to the formulas Read the glossary

Three scenarios, always

Every formula runs three times — pessimistic, realistic, optimistic — using different change rates. You see the full range of outcomes side by side.

Year-by-year, not averages

Taxes, expenses and returns are computed for each year individually. No smoothing, no single headline number hiding the truth.

Auditable by design

Every calculated row carries a SHA-256 checksum plus created/updated stamps. You can export the full workings to Excel or JSON at any time.

Advanced widgets

The widgets that do real mathematics — not just sums and group-bys. Each one lists its data inputs, the exact formula, a worked example, and the caveats we want you to know.

Net worth over time

The headline number. Market value of everything you own, minus everything you owe, charted year by year.

Inputs

  • • asset_market_amount (per asset, per year)
  • • mortgage_amount (per asset, per year)

Caveats

Uses your actual entered values up to the current year; future years come from the prognosis engine, not this widget.

Formula

\[ NW_y \;=\; \sum_{a \in A_y} M_{a,y} \;-\; \sum_{a \in A_y} L_{a,y} \]

\(NW_y\) net worth in year \(y\), \(M_{a,y}\) market value of asset \(a\), \(L_{a,y}\) mortgage balance, \(A_y\) all active assets for the chosen configuration.

Worked example

Year 2024 — assets total 8 450 000, mortgages total 3 200 000. \(NW_{2024} = 8\,450\,000 - 3\,200\,000 = 5\,250\,000\).

FIRE number & progress

How much wealth you need to retire — and how far you already are. The single most important number on the dashboard.

Inputs

  • • expence_amount (all assets, current year)
  • • asset_market_amount (liquid + preserved, current year)

Caveats

The 25× multiplier is the inverse of the 4% safe-withdrawal rule. For a more conservative plan, raise the multiplier (30× ⇒ 3.33% SWR).

Formula

\[ F \;=\; 25 \times E \qquad\quad p \;=\; \min\!\left(\tfrac{P}{F},\, 1\right) \]

\(F\) FIRE number, \(E\) annual expenses, \(P\) current portfolio value, \(p\) progress toward FIRE (0 to 1).

Worked example

Annual expenses 540 000, portfolio 7 200 000. \(F = 25 \times 540\,000 = 13\,500\,000\); \(p = 7\,200\,000 / 13\,500\,000 \approx 53.3\%\).

FIRE crossover point

The moment your portfolio can pay for your life from passive income alone. After this you are, in principle, free.

Inputs

  • • asset_market_amount (current year)
  • • expence_amount (current year)

Caveats

Binary indicator — not a sell-down simulation. For year-by-year withdrawal feasibility across three scenarios, the full prognosis engine runs a real liquidation against your actual assets and taxes.

Formula

\[ \text{crossover} \;\Longleftrightarrow\; 0.04 \cdot P \;\geq\; E \]

\(P\) current portfolio, \(E\) annual expenses. The 0.04 constant is the classic 4% safe-withdrawal rate.

Worked example

Portfolio 15 000 000, expenses 540 000. Passive income \(0.04 \times 15\,000\,000 = 600\,000 \geq 540\,000\) ⇒ crossover achieved.

FIRE metrics over 30 years

Projects net worth forward 30 years against an inflation-adjusted FIRE target, so you can see the year the two lines cross.

Inputs

  • • current net worth
  • • annual savings (\(I - E\))
  • • growth rate \(r = 7\%\)
  • • inflation \(\pi = 3\%\)

Caveats

Uses constant \(r\) and \(\pi\) for readability. The main prognosis engine runs the same projection per asset, per year, across three scenarios with configurable change rates.

Formula

\[ P_{t+1} \;=\; (P_t + S)(1 + r), \qquad F_t \;=\; F_0 \cdot (1 + \pi)^t \]

\(P_t\) projected portfolio in year \(t\), \(S\) annual savings (income minus expenses), \(r\) nominal growth rate, \(F_t\) FIRE number inflated from \(F_0\) by \(\pi\).

Worked example

Start \(P_0 = 5\,000\,000\), \(S = 300\,000\). After one year \(P_1 = (5\,000\,000 + 300\,000) \times 1.07 = 5\,671\,000\). After ten years \(P_{10} \approx 14\,020\,000\).

Savings rate over time

The single best predictor of your FIRE timeline. A 50% savings rate brings financial independence in roughly 17 years regardless of income.

Inputs

  • • income_amount (per year, income assets)
  • • expence_amount (per year, all assets)

Caveats

Historic years only — the widget never projects into the future. Negative when expenses exceed income (drawing down).

Formula

\[ s_y \;=\; \frac{I_y - E_y}{I_y} \]

\(s_y\) savings rate in year \(y\), \(I_y\) total income, \(E_y\) total expenses. Expressed as a percentage. Benchmark line drawn at 20%.

Worked example

Income 900 000, expenses 540 000. \(s = (900\,000 - 540\,000) / 900\,000 = 40\%\).

Retirement readiness

Projects today's net worth to your planned retirement age against a capital-adequacy target, using your own expense baseline.

Inputs

  • • current net worth
  • • birth_year, pension_wish_year, death_year
  • • annual income, annual expenses

Caveats

The 80% replacement ratio is a widely used rule of thumb, not a personal forecast. Pension payouts from tjenestepensjon/IPS/offentlig pensjon are modelled separately by the tax engine.

Formula

\[ T \;=\; 25 \times 0.80 \times E \qquad\quad NW_{t} \;=\; (NW_{t-1} + S)(1+r) \]

\(T\) retirement target (25× of 80% of current expenses — the classic 70–80% income-replacement rule), \(NW_t\) projected net worth at age \(t\), \(r\) assumed growth (default 7%).

Worked example

Expenses 540 000 ⇒ \(T = 25 \times 0.80 \times 540\,000 = 10\,800\,000\). Starting from 3 000 000 at age 40 with 300 000 annual savings, \(NW_{65} \approx 23\,100\,000\) — comfortably above target.

Actual effective tax rate

Your real tax burden — every tax the engine calculated, divided by taxable base. Not a headline rate, the rate you actually pay.

Inputs

  • • income_tax
  • • fortune_tax
  • • property_tax
  • • capital_gains_tax
  • • taxable_income_base

Caveats

Fortune tax and property tax are wealth-based but are included in the numerator because they are a real cash outflow. The ratio is not directly comparable to a marginal income-tax rate.

Formula

\[ \tau_y \;=\; \frac{T^{\text{income}}_y + T^{\text{fortune}}_y + T^{\text{property}}_y + T^{\text{gains}}_y}{B_y} \]

\(\tau_y\) effective tax rate in year \(y\), \(T^{\star}_y\) the tax paid of each kind, \(B_y\) the taxable base (gross income + realised gains).

Worked example

Gross base 950 000, total taxes 278 400. \(\tau = 278\,400 / 950\,000 \approx 29.3\%\).

Taxation

The tax engine models the real brackets, thresholds and shielding rules — not rough percentages. Rates, bands and municipal rules are loaded per year from the tax configuration tables.

Fortune tax (formueskatt)

\[ T^{\text{fortune}} \;=\; \max\!\bigl(0,\; W_{\text{net}} - W_{\text{threshold}}\bigr) \cdot \bigl(r_{\text{state}} + r_{\text{muni}}\bigr) \]

\(W_{\text{net}}\) valued net wealth (primary residence, shares, business assets each get their own valuation discount), \(W_{\text{threshold}}\) annual threshold, \(r_{\text{state}}\) and \(r_{\text{muni}}\) state and municipal rates.

Bracket tax (trinnskatt)

\[ T^{\text{bracket}} \;=\; \sum_{k=1}^{K} r_k \cdot \max\!\bigl(0,\; \min(Y, b_{k+1}) - b_k\bigr) \]

\(Y\) gross ordinary income, \(b_k\) lower bound of bracket \(k\), \(r_k\) marginal rate for that bracket. Brackets are loaded per year from the tax configuration.

Tax shield (skjermingsfradrag)

\[ S_t \;=\; C_t \cdot r^{\text{skjerm}}_t, \qquad T^{\text{dividend}} \;=\; \max\!\bigl(0,\; D_t - S_t\bigr) \cdot g \cdot r^{\text{cap}} \]

\(C_t\) cost basis, \(r^{\text{skjerm}}_t\) annual risk-free shielding rate, \(S_t\) shielding deduction, \(D_t\) dividend received, \(g\) gross-up factor (currently 1.72), \(r^{\text{cap}}\) capital tax rate.

Property tax (eiendomsskatt)

\[ T^{\text{property}} \;=\; \max\!\bigl(0,\; V \cdot d - V_{\text{threshold}}\bigr) \cdot r_{\text{muni}} \]

\(V\) property market value, \(d\) municipal valuation discount (often 0.70), \(V_{\text{threshold}}\) municipal bottom deduction, \(r_{\text{muni}}\) municipal rate. 327 municipalities ship configured.

Prognosis math

The primitives that roll every asset forward, year after year, across three scenarios.

Yearly compound roll-forward

\[ V_{y+1} \;=\; V_y \cdot \bigl(1 + c_{y,s}\bigr) \;+\; \Delta_{y,s} \]

Each asset evolves year by year. \(V_y\) value in year \(y\), \(c_{y,s}\) percentage change rate for year \(y\) under scenario \(s\), \(\Delta_{y,s}\) fixed-amount adjustments (top-ups, transfers, rule-engine mutations).

Compound Annual Growth Rate (CAGR)

\[ \text{CAGR} \;=\; \left(\frac{V_{\text{end}}}{V_{\text{start}}}\right)^{\!1/n} - 1 \]

Smoothed annualised growth between two points in time. \(n\) is the number of years. Used in simulation summaries and the asset overview card.

Real vs. nominal return

\[ r_{\text{real}} \;=\; \frac{1 + r_{\text{nominal}}}{1 + \pi} - 1 \]

Converts a nominal return into real (inflation-adjusted) return using CPI \(\pi\). The engine shows both; expenses and tax thresholds are inflated using the same \(\pi\).

Annuity mortgage payment

\[ A \;=\; L \cdot \frac{r\,(1+r)^{n}}{(1+r)^{n} - 1} \]

\(A\) annual payment, \(L\) remaining loan, \(r\) periodic interest rate, \(n\) remaining term. Every year splits into interest (tax-deductible) and principal.

Now run the numbers on your own life.

Every formula on this page runs live against your own assets, income, taxes and scenarios the moment you sign in. No spreadsheet, no guesswork.

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