Inspectable Arithmetic for the Simple Investment Calculator
Version 1.2
Last verified: August 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. Inflation adjustment, when enabled, is a display conversion into today's dollars and does not change the contribution path.
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
- FVnominal = nominal future value after compounding
- FVreal = inflation-adjusted future value in today's dollars
- i = annual inflation rate
- CFt = 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
i = (1 + r)1/n − 1
N = round(n × t)
FV = P(1 + i)N + PMT × ((1 + i)N − 1) / i
Rationale: Effective period rate from the annual return, then ordinary-annuity future value (contributions at end of each period). Equivalent to period-by-period simulation in the shared investment growth engine.
Limitation: Assumes constant return and deterministic compounding; does not model volatility, sequence-of-returns risk, or varying contribution schedules.
2. Inflation Adjustment (Display Only)
FVreal = FVnominal / (1 + i)t
Rationale: The real-dollars checkbox is a display control. Contributions stay the entered dollar amount for the whole horizon. Inflation is used only to express that same nominal path in today's dollars. This is equivalent to simulating with the shared engine flag indexContributionsToInflation: false and displaying finalBalanceReal.
Limitation: Assumes steady inflation and does not model year-to-year CPI variability. It also does not raise contributions with prices. The Inflation-Adjusted Investment Calculator indexes contributions instead.
3. Internal Rate of Return (If Displayed)
NPV = Σt=0T CFt / (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 a display assumption only: it converts the same fixed-contribution nominal path into today's dollars. Contributions are not indexed to inflation.
- 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
- Growth uses shared
InvestmentGrowthEngine.simulateInvestment() in /assets/js/investment-growth.engine.js.
- The periodic rate is the effective rate
i = (1 + r)1/n − 1 (not r/n).
- Supported contribution frequencies include annual, monthly, biweekly (26), and weekly (52).
- IRR (when displayed) is solved from the nominal cash-flow series in the page script and annualized. Toggling real display does not change the IRR.
- 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.
Sources and References