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MONEY UNDER THE HOOD // WEALTHSYNTAX.IO

Personal finance for engineers, explained as systems

Free short books and calculators that show how compounding, risk, and cash flow work, with the math visible.

01 // The math is shown

Every calculator lists its formula and assumptions, so you can check the result instead of trusting it.

02 // State Machine Model

Treat your balance sheet like a system: income in, spending out, a cash buffer for shocks, and investments that compound.

03 // No affiliate links

No affiliate links or sponsored content. Read our editorial policy.

INTERACTIVE RECURRENCE ENGINE

Simulate the Compounding State Machine

Adjust the control variables below to observe how repeated compounding grows capital faster over time.

State Parameters

$10,000
$0$50k$100k
$1,000/mo
$0/mo$2,500/mo$5,000/mo
8.0%
2% (Conservative)8% (illustrative, nominal)15% (high, not a forecast)
20 Years (240 cycles)
1 Year20 Years40 Years
Closed Form: A = P(1 + r/12)^(12t) + PMT · [((1 + r/12)^(12t) - 1) / (r/12)]

End State (t = 20y)

Projected Future Portfolio Value
$638,288
2.55x Multiplieron total capital contributed
Principal: $250,000 (39%)Interest: $388,288 (61%)
Crossover Milestone: Month 95 (Year 8)At Month 95 (~Year 8), the portfolio generates more monthly compound interest ($1,005) than your active monthly contribution ($1,000/mo). From this threshold forward, the asset works harder than your active labor.
Growth Interval Trajectory
Year 5
$88,375
Year 10
$205,142
Year 15
$379,107
Year 20
$638,288

Illustrative projection. Assumes a constant annual return, contributions at the end of each month, and no taxes, fees, or inflation. Actual returns vary and can be negative. Educational content, not financial advice.

FREE GOOGLE SHEETS TEMPLATE

Stock & ETF Condition Screener

Screen your 30-ticker watchlist against moving-average conditions (21-DMA and 200-DMA crossovers, uptrend alignment, 52-week highs) using 100% native GOOGLEFINANCE formulas. Zero add-ons, no coding required.

✓ 100% Native Formulas✓ 5-Sheet Architecture✓ Customizable Toggles
MONEY UNDER THE HOOD // FREE EBOOKS

Short Books Explaining the Mechanics of Wealth

First-principles guides designed for analytical minds. Unabridged online reading, verified formulas, and downloadable editions.

View All Series Volumes
The Money Loop - Money Under the Hood Book 01
Money Under the Hood · Book 01100% Free10–15 min read

The Money Loop

How compounding makes returns generate returns

Growth becomes part of what grows. When an investment earns a return, that return joins the capital base and begins earning returns of its own. Explore how compounding turns time into an exponent, why early growth feels imperceptible, and how Maya beats Leo by starting 10 years earlier.

Simple vs. Compound Growth comparison
Deconstructing FV = PV × (1 + r)ⁿ
Maya vs. Leo starting-early proof
The Rule of 72 doubling mental model
Buy the Average - Money Under the Hood Book 02
Money Under the Hood · Book 02100% Free14 min read

Buy the Average

Dollar-cost averaging, turned into a simple investing system

You do not need to predict tomorrow when your system is engineered to work across every market condition. Deconstructs dollar-cost averaging: the fixed-dollar effect, why volume-weighted cost per share is strictly lower than average price via the harmonic mean, Maya vs. Leo, and the compounding crossover milestone.

Fixed-Dollar Effect & unit accumulation
Harmonic mean vs arithmetic price
Converting market drops into discounts
The Crossover threshold (V* = C_annual ÷ r)
Read HTML BookBook Overview & TOC
Fault Tolerant - Money Under the Hood Book 03
Money Under the Hood · Book 03100% Free16 min read

Fault Tolerant

How diversification protects your portfolio from a single point of failure

In software engineering, we design production systems so one component can fail without bringing the entire application down. In this third volume of Money Under the Hood, we model portfolio diversification through fault tolerance: single points of failure, Maya vs. Leo concentration, the Zero Test, position-size scaling law, idiosyncratic vs. systematic risk, and the 30-stocks correlation trap.

Single Point of Failure (SPOF) portfolio deconstruction
The Zero Test: stress-testing asset collapse
Linear scaling law: Portfolio impact ≈ p% × L%
30-stock correlation trap and risk factors
Read HTML BookBook Overview & TOC
SYSTEM PARADIGMS

Four Systems Mental Models for Financial Capital

How technical principles map directly to capital preservation, growth dynamics, and risk control.

PARADIGM 01S_{t+1} = S_t(1 + r) + C

Compounding as Recursive State

Saving a fixed amount grows linearly: S(t) = S0 + C*t. Compounding introduces a non-linear recurrence relation where elapsed cycle count sits in the exponent. For example, contributing $500/month at a 7% annual return for 25 years (inputs: $0 principal, $500/mo, 7% return, 25 years; $150,000 contributed) yields $405,036. Starting 5 years later for 20 years (inputs: $0 principal, $500/mo, 7% return, 20 years; $120,000 contributed) yields $260,463—a difference of $144,573 in growth from just $30,000 in additional contributions.

Read Compound Interest Guide
Primary InvariantTime Horizon > Contribution Volume
PARADIGM 02R_{recovery} = L / (1 - L)

Downside Asymmetry & Volatility Drag

The average annual return overstates what you actually compound at when returns are volatile. A 50% loss requires a 100% gain just to return to parity; an 80% loss requires a 400% gain. In systems terms, ruin is an absorbing barrier: capital preservation strictly precedes return optimization.

Primary InvariantAbsorbing Barrier Avoidance
PARADIGM 03Order_t = Invariant_USD

Dollar-Cost Averaging as Algorithmic Execution

Discretionary market timing is high-latency, emotionally compromised speculation. Automating dollar-cost averaging operates like a deterministic cron job: scheduled idempotent execution that naturally acquires more units at local troughs and fewer at peaks.

Read Dollar-Cost Averaging Guide
Primary InvariantZero Emotional Latency
PARADIGM 04Buffer >= Max(Expense_shock)

Liquidity Buffers as Circuit Breakers

In distributed systems, unbuffered queues drop requests under peak stress. In personal finance, an unbuffered balance sheet forces emergency liquidations of compounding equities during market drawdowns. Cash reserves let you cover a shock without selling investments at a bad time.

View Liquidity Buffer in Glossary
Primary InvariantFault-Tolerant Redundancy