Inspectable Arithmetic for the Simple Investment Calculator

Version 1.0
Last updated: February 2026

Transparent arithmetic is the operating system of this calculator.

This document publishes the full formulae, computational structure, and assumptions used to generate the outputs displayed on the calculator page.

No opinions. No hidden assumptions. Just arithmetic.

Purpose

This calculator models deterministic compound growth with periodic contributions and optional inflation adjustment under constant nominal return assumptions.

Definitions

Let:

P = starting principal (initial investment)
PMT = contribution per period
r = nominal annual return (decimal)
n = number of compounding periods per year
t = number of years
FV = nominal future value
FV_nominal = nominal future value after compounding
FV_real = inflation-adjusted future value in today's dollars
i = annual inflation rate
CF_t = cash flow at time t
T = total number of periods

Formulae

The following equations define the computational structure of this calculator:

1. Compound Growth with Periodic Contributions

FV = P(1 + r/n)^nt + PMT × ((1 + r/n)^nt − 1) / (r/n)

Rationale: This is the standard closed-form future value equation for periodic contributions under constant compounding.

This form assumes contributions occur at the end of each contribution period (ordinary annuity).

Limitation: Assumes constant return and deterministic compounding; does not model volatility, sequence-of-returns risk, or varying contribution schedules.

2. Inflation Adjustment (Real Value)

FV_real = FV_nominal / (1 + i)^t

Rationale: Converts nominal future value to present purchasing power using a constant annual inflation rate.

Limitation: Assumes steady inflation and does not model year-to-year CPI variability or regime changes.

3. Internal Rate of Return (If Displayed)

NPV = Σ_t=0^T CF_t / (1 + r)^t = 0

Rationale: Internal Rate of Return (IRR) represents the discount rate that sets net present value of all cash flows equal to zero.

Limitation: Multiple IRR solutions can exist when cash flows change sign more than once; results assume conventional cash flow structure unless otherwise specified.

Assumptions

Returns are modeled as constant and deterministic over the full investment horizon.
Contributions are applied at the end of each contribution period unless explicitly stated otherwise on the calculator page.
Compounding frequency matches the contribution frequency used in the calculation.
Inflation, when enabled, is modeled as a constant annual rate.
No taxes, fees, transaction costs, or behavioral changes are applied unless explicitly included on the calculator page.
Values may be rounded for display purposes; internal calculations use full numerical precision.

Implementation Notes

The periodic rate is derived as r/n.
Nominal future value is calculated before any inflation adjustment is applied.
Inflation adjustment is applied after full nominal growth has been computed.
All computations are performed using floating-point arithmetic; rounding occurs only at the display layer.

If any discrepancy is identified between this documentation and the calculator output, the arithmetic here governs.