Hypothetical worked example and primary educational references; not observed market data.
An average needs a weighting question
A household with multiple savings balances may want one summary yield. FINRA's return discussion relates gains to the money committed, which suggests the correct weights for a simple fixed-balance example. An account holding more money contributes more to total interest than an equally yielding small account. An unweighted average gives each account the same influence regardless of its size. That may summarize the list of rates, but it does not summarize the household's money growth. State the question first: average quoted rate per account, or earnings divided by total funds? Those are legitimate but different measurements. The weighted method here addresses the second under a common one-year horizon and unchanged starting balances.
Supporting references: 1. FINRA: Return and rate of return
Calculate interest before combining rates
Multiply each starting balance by its comparable annual effective yield to obtain its modeled one-year interest. Add the interest amounts and divide by total starting money. The worked example has USD 2,000 earning five percent and 8000 earning two percent. Its weighted result can also be calculated by applying each balance's share of the total to its percentage. The table contrasts that result with the simple mean of the two rates. The simple mean overstates the money-weighted outcome because the larger balance earns the lower rate. Reversing the balances would reverse that tendency. The error is not inherent optimism in averaging; it comes from assigning weights that do not match the quantity being summarized.
Hypothetical worked example
Two balances receiving different hypothetical annual yields
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.
- USD 2,000 earns 5%, while USD 8,000 earns 2% for one year.
- No cash flows, taxes, or fees; both rates are effective annual yields.
- Comparison row uses an unweighted average of the two percentages.
Calculated annual yield or mean (%)
- Balance-weighted yield2.60
- Unweighted arithmetic mean3.50
Shared zero-based scale; negative values extend to the left.
- Lowest displayed value
- 2.60
- Highest displayed value
- 3.50
Hypothetical cases from the table below, in the stated units. Not market observations, a forecast or a recommended choice. Read the scenario assumptions before comparing.
| Hypothetical scenario | Calculated annual yield or mean (%) |
|---|---|
| Balance-weighted yield | 2.60 |
| Unweighted arithmetic mean | 3.50 |
Calculation details
- Balance-weighted yield
- 2.60 percent balance-weighted one-year yield
((((2000 * 0.050000000000000003) + (8000 * 0.02)) / 10000) * 100) - Unweighted arithmetic mean
- 3.50 percent unweighted mean annual yield
((5 + 2) / 2)
A weighted result should fit between its inputs
With nonnegative balances and weights summing to one, the weighted average lies between the lowest and highest component rates. That is a useful arithmetic check. A result outside the range signals a unit error, omitted balance, negative weight, or a different measurement such as a leveraged cash-flow return. Another check is to multiply the blended rate by total starting money and confirm that it reproduces total modeled interest. These checks do not establish that the input rates are available or that future growth will occur. They test internal consistency only. The example's rates are invented, so the weighted result remains a mathematical summary of assumptions rather than evidence about the household's actual account earnings.
Date differences can defeat a static weight
If money enters one account halfway through the year, its opening or closing balance is not automatically the correct annual exposure weight. A static average can then overstate or understate earnings. Track how long each amount participates in each rate, using actual growth methods when compounding matters. Transfers between accounts also require care: money leaving one balance and entering another should not be counted in both for the same time interval. The fixed-balance example avoids these complications. A real household summary may need a cash-flow ledger or period-by-period model rather than one balance-weighted percentage. The weights must represent the exposure relevant to the question, not whichever snapshot is easiest to retrieve.
A blended yield does not blend account conditions
CFPB's APY framework makes annual interest measures comparable under stated assumptions, but account access, fees, and eligibility remain separate. A mathematical average cannot tell whether all money is available tomorrow or whether every balance has the same applicable protection. It also cannot incorporate charges unless they are explicitly included in net earnings. The table excludes those features and uses matching annual effective inputs to isolate weighting. A useful summary keeps component balances and rates visible alongside the blended result. That allows the reader to reproduce the money-growth measure while still assessing each balance's purpose and terms. The lesson is to weight by the quantity that generates the outcome, then preserve the conditions that an average necessarily compresses.
Supporting references: 2. CFPB: Regulation DD, Appendix A
Test another situationA transfer changes weights without changing household principal
A separate hypothetical case. Its inputs differ from the main worked example above.
A transfer changes weights without changing household principal
Suppose hypothetical USD 1,000 earns an invented 6% effective annual yield and USD 3,000 earns 2%, with both held unchanged for one year. Total interest is USD 120, a 3% blended yield on USD 4,000. If USD 1,000 moves from the lower-yield account to the higher-yield account before the year starts, interest becomes USD 160 and the blend becomes 4%. The transfer creates no principal; it changes exposure and adds USD 40 of modeled interest. The trade-off is that assumed earning improvement against any actual differences in access, qualifying balance rules, and transfer costs, all excluded from this sensitivity.
Test the weighted summary by rebuilding currency earnings
FINRA defines percentage return relative to committed money. A valid blended summary should reproduce total currency gain when multiplied by the corresponding total principal. It should also stay between the component rates when weights are nonnegative and the measurement period matches. If deposits or transfers occur during the year, a static closing-balance blend can assign exposure that never existed. Use each dated period or lot instead. An unweighted average describes the list of account rates, while a balance-weighted figure describes the selected money boundary. Neither average merges different account conditions or establishes that every unit can be moved without consequences.
Supporting references: 1. FINRA: Return and rate of return
Check this case’s calculations
- Initial combined interest
- 120.00 USD
((1000 * 0.059999999999999998) + (3000 * 0.02)) - Initial blended yield
- 3.00 percent
((120 / 4000) * 100) - Interest after reallocation
- 160.00 USD
((2000 * 0.059999999999999998) + (2000 * 0.02)) - Reallocated blended yield
- 4.00 percent
((160 / 4000) * 100) - Additional interest
- 40.00 USD
(160 - 120)
Limits of this additional case
- The transfer occurs before all earning periods; midyear transfers require a dated model rather than these static weights.
Limits of this analysis
- Changing balances require a dated cash-flow or exposure model.
- Costs and taxes can differ across accounts.
- A blended mathematical yield does not unify access or protection terms.
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.
- CFPB: Regulation DD, Appendix A
APY annualizes interest relative to principal and term under specified assumptions.
Scope: US covered deposit disclosures; not a universal account formula.. Reference accessed 2026-10-06.
Illustrative calculations are not forecasts or personal recommendations. Editorial standards
