Inspect the Arithmetic — Compound Interest Multipliers
Version 1.0
Last verified: August 2026
Transparent arithmetic is the operating system of this calculator.
This document publishes the formula, grid construction, and display rounding used to generate the compound interest multipliers table.
No opinions. No hidden assumptions. Just arithmetic.
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Purpose
The page is a static grid of growth factors. Each cell is how many times larger an amount becomes after compounding at a fixed annual rate for a stated number of years. Multiply any starting amount by the cell value to get a future value under those assumptions.
Definitions
Let:
- r = annual rate as a decimal (the table labels rates as percents: 1% is r = 0.01)
- t = number of years (integer)
- M(r, t) = compound interest multiplier
Formulae
1. Multiplier
M(r, t) = (1 + r)t
Rationale: One compounding event per year at a constant rate. The script computes Math.pow(1 + r, y) for each cell.
Limitation: This is nominal growth only. It does not include inflation, taxes, fees, or cash flows.
2. Grid range
The published table is fixed:
- Annual rates: 1% through 15% in 1 percentage-point steps
- Years: 0 through 50 inclusive
At t = 0, M = 1 for every rate. That is the identity: no elapsed compounding periods.
3. Worked example
At 7% for 30 years:
M = (1.07)30 ≈ 7.612255
$10,000 × 7.612255 ≈ $76,123. The table stores the multiplier, not a dollar amount.
4. Display rounding
Internal values use full floating-point precision. Display formatting is:
- Exact integers (including every year-0 cell) are shown without decimals.
- Values ≥ 1,000 are shown with 6 significant figures.
- Other values are shown with up to 9 decimal places, with trailing zeros stripped.
Rounding is cosmetic. Recalculating (1 + r)t independently should match the unrounded value, not necessarily the trimmed cell text.
Assumptions
- Annual compounding once per year. No monthly or continuous compounding.
- Constant rate for the full horizon. No path, volatility, or sequence of returns.
- No starting principal is required. The cell is a pure multiplier.
- No inflation adjustment, taxes, fees, contributions, or withdrawals.
- Share-scenario links encode a selected rate and year; they do not change the formula.
Implementation notes
- The grid is built in
calculators/compound-multipliers/script.js.
- There is no separate engine file. The page script is the arithmetic.
If any discrepancy is identified between this documentation and the table, the formula (1 + r)t governs.