Hypothetical worked example and primary educational references; not observed market data.
A fee formula needs a balance definition
A percentage fee scales with a specified balance, but the phrase one percent fee leaves that base unstated. It could refer to an opening balance, an average, a closing value, or another contractual measure. FINRA's return discussion recognizes costs as part of interpreting gains. To model a balance charge, identify the base and the deduction date separately from the growth assumption. A fee assessed after interest can remove more currency than the same percentage assessed on the opening balance. Neither method is universally implied by the percentage alone. The example uses a deliberately hypothetical post-growth charge to show the mechanism, without suggesting that a particular savings account or financial service applies that structure.
Supporting references: 1. FINRA: Return and rate of return
Use successive factors for a post-growth charge
If annual gross growth is four percent and one percent of the resulting balance is then deducted, multiply by 1.04 and then by 0.99. The combined factor is 1.0296. Subtracting the fee percentage from the gross growth percentage would give three percent, a slightly different result. The discrepancy comes from charging the percentage on the enlarged balance. The example applies this same sequence for five years to a hypothetical starting balance of USD 10,000. One row has no charge; the other applies the annual post-growth deduction. Both retain all remaining money. The ending difference includes direct charges and the later growth that those removed units no longer earn.
Hypothetical worked example
A hypothetical annual balance charge over five years
Model setup
Read these assumptions before comparing the scenarios.
- All monetary amounts in this example are hypothetical U.S. dollars (USD), not current prices, quoted account terms or observed market data. Percentages, counts, time periods and index levels retain their stated units.
- Start with USD 10,000 and 4% annual gross growth.
- A 1% balance charge is deducted after growth each year.
- Compare five years with and without the charge; no taxes, contributions, or other costs.
Calculated result (USD)
- 1. No annual balance charge
- 12,166.53
- 2. 1% deducted after growth
- 11,570.25
Expanded comparison scale, not zero-based. Range: 11,450.99 to 12,285.79, in the units above. Case numbers match the labels; no probability or time trend is implied.
Hypothetical model, not observed market data or a forecast. Assumptions above; original values and calculations below.
| Hypothetical scenario | Calculated result (USD) |
|---|---|
| No annual balance charge | 12,166.53 |
| 1% deducted after growth | 11,570.25 |
Calculation details
- No annual balance charge
- 12,166.53 USD
(10000 * (1.04 ^ 5)) - 1% deducted after growth
- 11,570.25 USD
(10000 * ((1.04 * 0.98999999999999999) ^ 5))
Changing the base changes the result
If the fee instead equals one percent of each year's opening balance, the net one-year factor under the same gross growth assumption is 1.03. That alternative answers a different contractual question. With fees deducted monthly, another path arises because each deduction affects the balance available for later monthly growth. A model should not choose whichever ordering produces the most favorable result. It should reproduce the stated structure and then explain its consequences. Sequential factors are powerful because they make the order and base explicit. But their convenience depends on the fee being proportional to the balance at that exact point. Fixed charges, minimum charges, and caps require additional cash-flow rules rather than a single multiplicative factor.
Longer horizons reveal the indirect cost
The balance removed by a fee cannot participate in subsequent growth, so the cumulative gap between fee and no-fee paths generally exceeds the sum of some early charges viewed in isolation. The magnitude depends on the assumed growth and dates. Calling every difference lost return can obscure whether it came from a fee itself or the growth exposure removed by the fee. A useful comparison records both paths consistently and values them at the same endpoint. The table does that under fixed assumptions. It does not estimate the empirical effect of fees on actual consumers or imply that removing a service charge leaves all other terms unchanged. The no-fee row is a mathematical control, not necessarily an available alternative.
Compare net outcomes with clear boundaries
Investor.gov's growth calculator supplies a framework for principal, time, and estimated rates; fees require an additional explicit rule when they are not already reflected in the input. Avoid deducting the same charge twice by using both a net growth rate and a separate fee factor. Equally, do not omit a charge by labeling a gross rate as net. The example excludes taxes, new deposits, and every other cost, so its five-year values isolate one mechanism. For a practical comparison, use the actual disclosed fee base and dates and test the balance levels the saver expects. The resulting statement should explain both the gross assumption and the deduction rule so a precise final figure does not conceal how the available money was calculated.
Supporting references: 2. SEC Investor.gov: Compound Interest Calculator
Test another situationA terminal contribution changes the fee base
A separate hypothetical case. Its inputs differ from the main worked example above.
A terminal contribution changes the fee base
Imagine hypothetical USD 2,000 grows 5% over one year, then receives a USD 1,000 contribution immediately before an invented 1% charge on the entire resulting balance. The endpoint is USD 3,069. If the same contribution arrives immediately after the charge, the endpoint is USD 3,079. The USD 10 difference is the charge on new principal that earned no modeled return before assessment. Both paths contribute the same amount and assume no other costs. The trade-off is the timing of adding money relative to a balance-based deduction, not account performance. Actual terms would determine whether such timing changes the assessed base at all.
Reconcile the percentage with the contractual base
FINRA notes that costs affect return interpretation. Extend that principle by recording the balance to which a percentage charge applies and the point in the sequence when it is assessed. A quoted annual percentage cost does not identify whether new deposits, average balances, or only an opening balance are charged. Do not subtract the fee again if the input growth rate already includes it. Conversely, calling a gross rate net does not make the charge disappear. For models with changing balances, a dated sequence reveals which units pay the fee and prevents new contributions from being mistaken for earnings when comparing endpoints.
Supporting references: 1. FINRA: Return and rate of return
Check this case’s calculations
- Contribution before assessment
- 3,069.00 USD
(((2000 * 1.05) + 1000) * 0.98999999999999999) - Contribution after assessment
- 3,079.00 USD
(((2000 * 1.05) * 0.98999999999999999) + 1000) - Contribution timing fee difference
- 10.00 USD
(3079 - 3069)
Limits of this additional case
- The stipulated fee applies to the assessment-date balance; actual percentage charges may use averages or other bases.
Limits of this analysis
- Actual percentage charges may use average, opening, or other balances.
- Real deposit accounts need not use this hypothetical fee structure.
- Charges and growth rates may change over time.
Sources and scope
- FINRA: Return and rate of return
Percentage return relates gain to the amount committed; inflation and costs affect interpretation.
Scope: US investor education; no portfolio or product recommendation.. Reference accessed 2026-10-06.
- SEC Investor.gov: Compound Interest Calculator
Growth illustrations distinguish time, contributions, estimated rate, and compounding frequency.
Scope: US educational calculator; assumptions are not forecasts.. Reference accessed 2026-10-06.
Illustrative calculations are not forecasts or personal recommendations. Editorial standards
