Inspect the Arithmetic — Flat-Fee or Hourly Advisor Cost Calculator

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 estimates the long-run effect of flat-fee, hourly, or percentage-of-assets (AUM) advisor fees on a portfolio. It decomposes the total impact into direct fees paid, lost compounding from removing those dollars, the gap between ending values with and without fees, and an AUM-fee percentage that would produce the same ending value as a given flat or hourly schedule.

Definitions

Let:

B₀ = starting portfolio balance (initial value)
B_t = portfolio balance at the end of month t
C = monthly contribution (dollars added at end of month)
F = annual advisor fee in dollars (flat-fee or hourly model before monthly conversion)
T = time horizon in years
N = 12T = total number of months
r = annual nominal return (decimal)
r_m = effective monthly return derived from r
f_a = annual advisor fee rate (decimal, for AUM model)
Fee_t = fee dollars deducted in month t
TotalFees = Σ Fee_t over the full horizon
FV_without = ending value with no advisor fees
FV_with = ending value with the chosen fee model
TotalCost = FV_without − FV_with
LostCompounding = TotalCost − TotalFees

Core Equations

1. Monthly Return from Annual Return

The calculator converts the user-supplied annual nominal return r into an effective monthly rate r_m:

r_m = (1 + r)^1/12 − 1

2. Growth Without Advisor Fees

With no advisor fees, the portfolio is simulated month by month with contributions at the end of each month:

B₀ = startingBalance
For t = 1, 2, …, N:
B_t = B_t−1(1 + r_m) + C

The ending value without fees is:

FV_without = B_N

3. Growth With Flat, Hourly, or AUM Fees

With advisor fees, the simulation still runs month by month with growth first, then fees, then contributions at the end of the month.

Growth step (all models):

B_t^gross = B_t−1(1 + r_m)

Fee step depends on the model:

Flat-fee model: a flat annual fee F (optionally increased by a fixed percentage each year) is converted to a monthly fee F/12 and deducted each month.
Hourly model: an hourly rate × hours per year defines an annual dollar fee, again converted to a monthly amount and optionally increased each year.
AUM model: a percentage-of-assets rate f_a (annual decimal) is applied as a monthly percentage of the current balance:
f_a,m = f_a / 12
Fee_t = B_t^gross × f_a,m

In all cases, the fee deducted in month t is:

Fee_t = monthly fee determined by the chosen model, capped so it cannot exceed B_t^gross
B_t^net = B_t^gross − Fee_t

Contribution step (all models):

B_t = B_t^net + C

Total fees are tracked as:

TotalFees = Σ_t=1^N Fee_t

The ending value with fees is:

FV_with = B_N

4. Total Cost, Fees Paid, and Lost Compounding

The calculator defines the total cost of the fee model as the gap between ending values with and without fees:

TotalCost = FV_without − FV_with

Given TotalFees from the monthly simulation, lost compounding is the residual:

LostCompounding = TotalCost − TotalFees

5. AUM-Fee Equivalent

For flat and hourly models, the calculator finds the AUM fee rate f_a^* (annual decimal) that would produce the same ending value as the modeled schedule, holding all other inputs constant. It does this numerically using a binary search on an AUM rate between 0 and 5%.

Let FV_{with_AUM(f)} be the ending value from the AUM fee simulation with rate f. The calculator searches for f such that:

FV_{with_AUM(f)} ≈ FV_with

If no solution is found below 5% (i.e., even a 5% AUM fee does not reduce the portfolio as much as the modeled flat or hourly schedule), the calculator reports an AUM-equivalent of “≥ 5.00%”.

Implementation Notes

The core arithmetic is implemented in calculateFlatFeeOrHourlyCost() inside /calculators/flat-fee-or-hourly/engine.js, which calls helper functions to simulate paths with and without fees and to solve for the AUM-equivalent rate.
Contributions are always applied at the end of each month after growth and fee deduction, matching the description above.
All calculations use JavaScript’s standard floating-point arithmetic; any rounding is applied only when formatting numbers for display.

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