Hypothetical worked example and primary educational references; not observed market data.
A temporary rate describes only part of the timeline
An introductory savings rate can be attractive while covering only a small part of the intended holding period. CFPB's APY appendix addresses stepped and introductory-rate structures in the US disclosure context. A mathematical comparison should therefore model the complete path rather than extend the opening rate across the year. Identify the introductory duration, the assumed later rate, and any conditions affecting eligible balances. The later assumption deserves particular attention if it is variable. A clearly stated temporary rate is not itself misleading; the mistake occurs when a reader treats it as a full-horizon input without checking the time limits. The example makes both phases explicit so the headline and the complete earnings calculation remain distinct.
Supporting references: 1. CFPB: Regulation DD, Appendix A
Weight simple rates by their time exposure
When principal stays fixed and interest does not compound within the year, calculate each phase's interest using its fraction of the year, then add the phase amounts. The worked example uses USD 7,000 an invented six-percent annual rate for three months, and two percent for the next nine. Its comparison uses three percent for the whole year. The table values each complete path over twelve months. A straight average of six and two percent would treat the phases as equally long, which they are not. The correct simple blending weights the rates by three-twelfths and nine-twelfths. The resulting equality in this example is a designed arithmetic demonstration, not an observation about current promotional accounts.
Hypothetical worked example
Temporary rate versus a constant-rate mathematical benchmark
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.
- Principal is USD 7,000 with no cash flows or within-year compounding.
- First three months earn 6% simple annual interest; next nine earn 2%.
- Comparison earns 3% simple annual interest for twelve months; all terms are invented.
Calculated result (USD of one-year interest)
- 6% for three months, 2% for nine210.00
- 3% for the whole year210.00
Shared zero-based scale; negative values extend to the left.
- Lowest displayed value
- 210.00
- Highest displayed value
- 210.00
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 result (USD of one-year interest) |
|---|---|
| 6% for three months, 2% for nine | 210.00 |
| 3% for the whole year | 210.00 |
Calculation details
- 6% for three months, 2% for nine
- 210.00 USD of one-year interest
(((7000 * 0.059999999999999998) * 0.25) + ((7000 * 0.02) * 0.75)) - 3% for the whole year
- 210.00 USD of one-year interest
(7000 * 0.029999999999999999)
Compounding changes the phase connection
If earnings are retained and become part of the later phase's base, multiply the phase growth factors instead of merely adding simple interest on the unchanged principal. The appropriate factor depends on how the rate is defined and how interest compounds within each phase. A nominal annual rate may require a periodic division and a matching period count. An effective annual yield may require a fractional-power conversion for an idealized model. The table avoids these complications by explicitly assuming simple interest without within-year compounding. That boundary is important because a time-weighted arithmetic average can be exact for one simplified setup and only an approximation for another. A method should follow the stated earning mechanism, not the convenience of a single average.
Balance conditions can matter more than the headline
A high introductory rate might apply only to part of a balance, only to qualifying funds, or only while certain conditions hold. A saver should assign each unit to its actual rate exposure and period. If money enters after the introductory window begins, it may experience fewer high-rate days than the initial deposit. Fees or access conditions can also affect the net result. None of these details is supplied by the headline percentage alone. The hypothetical example excludes every eligibility rule and keeps the balance unchanged. Its purpose is to teach time weighting. A practical worksheet should add the actual applicable balance, dates, and costs rather than use the example's deliberately clean phases as an account forecast.
Treat the later rate as a scenario if it is unknown
US account-disclosure rules address variable-rate information and the periods during which specified rates apply. That framework helps a reader distinguish fixed introductory terms from an uncertain later path. For planning, calculate several clearly labeled post-introductory scenarios if the future rate is not fixed. Avoid replacing uncertainty with the most favorable assumed continuation. Compare the full-year net amounts and the dates on which money is needed. The table freezes the later rate and excludes costs, so its equality is conditional. Its enduring lesson is that a complete holding-period calculation needs every phase's duration and rate basis. A temporary headline can be understood accurately when it is placed inside that whole path rather than promoted into a year-long promise.
Supporting references: 2. CFPB: Regulation DD account disclosures
Test another situationLater money misses the opening-rate window
A separate hypothetical case. Its inputs differ from the main worked example above.
Later money misses the opening-rate window
Assume a hypothetical account pays simple annual interest of 8% for the first quarter-year and 2% for the remaining three quarters. USD 2,000 is present from the start, and an additional USD 1,000 arrives exactly when the introductory window ends. Original principal earns USD 70 over the year and later money earns USD 15, totaling USD 85. Applying the full-year time-weighted rate to the final USD 3,000 would instead imply USD 105, overstating interest by USD 20. No compounding or fees are included. The trade-off is retaining cash elsewhere during the opening window versus giving that cash exposure to the higher assumed rate.
Promotional time and balance eligibility are separate filters
CFPB's account-disclosure framework addresses rate periods and balance conditions. A complete promotional model assigns each deposit both an eligible interval and an eligible rate band. An account-level introductory end date does not restart merely because new funds arrive, unless the actual terms say so. Likewise, a balance cap can prevent part of the opening deposit from receiving the headline rate. Keep the post-introductory rate conditional if it can change, and compare the full holding period with a genuinely feasible alternative. A blended figure can summarize a fixed balance, but it cannot automatically describe money deposited after the attractive interval has already passed.
Supporting references: 2. CFPB: Regulation DD account disclosures
Check this case’s calculations
- Original money's annual interest
- 70.00 USD
(((2000 * 0.080000000000000002) * 0.25) + ((2000 * 0.02) * 0.75)) - Late deposit interest
- 15.00 USD
((1000 * 0.02) * 0.75) - Total correctly timed interest
- 85.00 USD
(70 + 15) - Final-balance blending shortcut
- 105.00 USD
(3000 * ((0.080000000000000002 * 0.25) + (0.02 * 0.75))) - Shortcut overstatement
- 20.00 USD
(105 - 85)
Limits of this additional case
- The introduction ends on an account-wide date and simple interest is assumed; actual promotions may use other eligibility or compounding rules.
Limits of this analysis
- Actual introductory disclosures may use specified APY methods and compounding.
- The post-introductory rate may change rather than remain fixed.
- Eligibility, balance caps, fees, and withdrawals are excluded.
Sources and scope
- 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.
- CFPB: Regulation DD account disclosures
Covered account disclosures address rates, balance methods, fees, and time-account conditions.
Scope: US Regulation DD; educational discussion does not establish individual legal rights.. Reference accessed 2026-10-06.
Illustrative calculations are not forecasts or personal recommendations. Editorial standards



