Floor 3 · The Engine Room

The math, shown

SI Money Tracker works out the figures in your plan with its own math engine and puts the equation one tap away on cards across the app.

This floor shows how the engine works, how we test it, what runs on your iPhone, and what is not yet released or not yet built.

Gauge 1 · Show the math

The equation behind the figure

Cards across the app carry a Show the math disclosure. Open it and you see the formula, the inputs that went in, the result with its unit, and where each number came from. It covers the surplus check, debt-to-income, spending limits, loan payoff and compound interest, among others.

When a figure comes from your bank rather than from the app, the disclosure says so: it was reported by your bank, not computed by the app. Not every figure has a disclosure yet; the ones that do show the equation that actually ran.

Show the math

Example A $4,200 card balance at 24.9 % APR, no new charges, interest charged monthly at APR ÷ 12.

r = 24.9 % ÷ 12 = 2.075 % per month
first month's interest = $4,200 × 0.02075 = $87.15

In words: the monthly rate is the yearly rate divided by twelve, and the first month's interest is the balance times that rate.

n = −ln(1 − r·B ÷ P) ÷ ln(1 + r)
P = $105: n = 86.28 → 87 payments, the last one $29.49
P = $250: n = 20.87 → 21 payments, the last one $217.91

In words: the number of months, n, depends on the balance B, the payment P and the monthly rate r. A fraction of a month becomes one smaller final payment.

Paying today's $105/month minimum, held at that amount, takes 87 months and $4,859.49 in interest. A $250/month plan takes 21 months and $1,017.91: 66 months and $3,841.58 less. Interest is summed month by month, rounded to the cent.

These are the app's Projection assumptions: a fixed payment, no new charges and a fixed APR. Card issuers usually charge interest daily, so a statement can differ.

Gauge 3 · The scientific calculator

A scientific calculator with its sources

Inside the app, under About › Tools, is a full scientific calculator with Basic, Graph, Stats and Sensors modes. It comes with the app at no extra charge and isn't part of Plus.

You can call 129 functions by name from the entry line: core math and trigonometry, physics (kinematics, forces, energy, gases, pendulums, drag), statistics, unit conversions, angles, map grids, dive pressure, color and loans. Each one is documented with its formula and the unit every input expects.

Function Reference. Search any function or constant (the search ignores accents, so “raiz” finds “raíz”). Each row shows the formula and the unit of every input and of the result, and VoiceOver reads them, for example “x in meters”.
Constants with sources. Physical constants use CODATA 2022 values. Each row says whether its value is exact by definition, measured (with its standard uncertainty) or rounded.
Physics tables. Fundamental constants, physical data, SI base and derived units, unit symbols, math symbols and the Greek alphabet.
School math. 50 equations from kindergarten to high-school statistics, in 8 grade bands, with a solver for a system of two linear equations that says “No unique solution” when the lines are parallel.
Graph and Stats. Plot one y = f(x) curve and trace exact points; undefined points stay as real gaps, with a note. Stats gives n, sum, mean, median, both standard deviations, both variances, minimum and maximum, and says how many of your entries it used.

Gauge 8 · On your iPhone

Your plan runs on your iPhone

Your plan's math is worked out on the phone: its totals, the monthly surplus check and the health checks. The full plan is stored on your iPhone, in a file iOS keeps closed while the phone is locked, and it is included in your own iPhone backup, on purpose. The app doesn’t send the plan itself to our server; while “Keep my plan’s monthly totals” is on, it sends each month’s totals.

“Keep my plan's monthly totals” starts on for a new account: that month's totals are saved with your account's monthly history. You can turn it off in Account settings › Monthly history; it then stays off for your account, on every phone.

With Plus, on-device models also label recurring charges in your linked-bank data, on the phone. Today those labels appear only in the Complete report when you export your plan; the lists you see on screen come from our rule-based detector. We don't publish an accuracy figure.

Bank sync, the live cards and the trackers that sync with your account need our own server. Traffic between the app and the server uses HTTPS. On the server, bank access tokens, code-app secrets and monthly history records are encrypted at rest; some transaction and card-detail fields are not yet. The app shows no advertising and has no third-party analytics or crash-reporting software.

What the server keeps, on Floor 2: The Vault

Where each kind of figure is worked out
Figure	On your iPhone	On our server
Your plan	Totals, the surplus check and the health checks	Not computed there; monthly totals are saved while that option is on (it starts on)
Calculator and labs	The 129 functions, Color Lab, sensors and Measure mode	The outdoor-temperature row, when you're signed in
Bank data (Plus)	Sorting into your plan and the subscription labeller	Bank connection and sync
Live cards	Displayed here, not worked out here	The weather card's backup reading, sun and moon, markets, benchmark figures and synced trackers, recorded in your Equation Ledger

Gauge 10 · How we test the math

Checked against the original spreadsheet

The budget began as a spreadsheet. Its 378 budget scenarios were generated from a model of that spreadsheet and checked against it; 113 loan-payoff and 57 savings-goal scenarios come from a model of the app's own engine. That makes 548 scenarios, each with its expected results: about 48,000 expected values in all. Our test runner replays every scenario against the app's own engine whenever we run verification, and the plan's currency totals must match exactly, to the cent.

Separate test files cover the physics, statistics and color-science math.

This is test infrastructure: it is how we check our own work. It isn't a screen in the app, and it isn't a count of calculations the app does for you.

The roof

Check the math yourself

Your plan, worked out on your iPhone, with the equation one tap away.

Get SI Money Tracker Coming soon

The budget comes with the app, no account needed. Plus adds bank connection and automatic import: 7 days free when Apple says you're eligible, then $9.99/month, billed through your Apple Account. Cancel anytime in Settings.