Inspect the Arithmetic — Cost of a 0.5% Annual Fee

Version 1.0
Last updated: March 2026

Transparent arithmetic is the operating system of this calculator.

This document publishes the 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 compares the ending value of an investment with no annual fee versus the ending value with a 0.5% annual fee, under the same “net = gross − fee” return model as the 1% page. It uses annual compounding and optional end-of-year contributions and reports the dollar gap and percentage reduction due to the fee.

Definitions

Let:

P = starting balance (initial principal, CAD)
c = annual contribution (CAD), applied at the end of each year
t = investment horizon in years
r_gross = gross annual return (decimal)
f = annual fee rate (decimal)
r_net = net annual return after fee (decimal)
FV_{no_fee} = ending value with no fee
FV_{with_fee} = ending value with fee
ΔFV = dollar difference = FV_{no_fee} − FV_{with_fee}
PctReduction = ΔFV / FV_{no_fee}

Core Equations

1. Future Value with Annual Compounding

As with the 1% calculator, both paths use the same annual-compounding future value formula with end-of-year contributions:

FV(P, r, t, c) = P(1 + r)^t + c · \frac{(1 + r)^t − 1}{r}, if r ≠ 0
FV(P, 0, t, c) = P + c · t, if r = 0

2. Ending Value with No Fee

With no fee, the calculator uses r_gross directly:

FV_{no_fee} = FV(P, r_gross, t, c)

3. Ending Value with a 0.5% Annual Fee

Under the “net = gross − fee” model, a 0.5% annual fee is a constant drag on the annual return:

f = 0.005
r_net = r_gross − f
FV_{with_fee} = FV(P, r_net, t, c)

4. Dollar Difference and Percent Reduction

The reported impact is:

ΔFV = FV_{no_fee} − FV_{with_fee}
PctReduction = \frac{ΔFV}{FV_{no_fee}}

Implementation Notes

The 0.5% and 1% calculators share the same engine functions TLM_FeeMath.fvAnnual and TLM_FeeMath.endingValueWithFee() in /assets/js/fee-math.js and the same UI wiring in initFeeCostPage() in /assets/js/fee-ui.js. Only the default feePct differs between pages.
All other notes on compounding, contribution timing, and display rounding are identical to the 1% methodology page.

If any discrepancy is identified between this documentation and the live calculator engine, the engine’s arithmetic (TLM_FeeMath + initFeeCostPage()) is the source of truth. This page will be updated to match the engine.