Hypothetical worked example and primary educational references; not observed market data.
A contribution increase is a separate assumption
Some savings plans begin with smaller deposits and increase them after a predictable expense ends or income changes. Investor.gov's goal framework helps relate contributions to a deadline, but a single monthly average can conceal the actual pattern. A stepped model records each phase's deposit amount and dates. It also separates confidence in future saving capacity from confidence in future interest. An expected raise is not money already available. A plan relying heavily on larger later deposits should identify the event that permits them and a fallback if it does not occur. The arithmetic can describe the intended schedule exactly while the feasibility of that schedule remains a distinct question for the household.
Supporting references: 1. SEC Investor.gov: Savings Goal Calculator
Value the first phase at its own endpoint
For six equal month-end deposits in the first phase, use the ordinary-annuity accumulation factor for six periods. That gives the balance at the end of month six. If those funds remain in the account, grow that subtotal for the six additional periods until the final valuation at month twelve. The second phase's deposits are valued directly at month twelve with their own six-period factor. Add the two subtotals. This sequence prevents a common timing error: adding the first phase's month-six total to the second phase's month-twelve total without allowing the early money to grow during the later phase. Every subtotal should carry both its units and its valuation date.
Hypothetical worked example
A two-phase contribution plan compared with equal deposits
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.
- Zero starting balance and 0.3% hypothetical monthly effective growth.
- First six month-end deposits are USD 100; next six are USD 250.
- Comparison uses twelve equal month-end deposits of USD 175; contributed totals match.
Calculated result (USD)
- 1. 100 then 250, six months each
- 2,126.78
- 2. 175 every month
- 2,135.00
Expanded comparison scale, not zero-based. Range: 2,125.14 to 2,136.64, 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) |
|---|---|
| 100 then 250, six months each | 2,126.78 |
| 175 every month | 2,135.00 |
Calculation details
- 100 then 250, six months each
- 2,126.78 USD
(((100 * (((1.0029999999999999 ^ 6) - 1) / 0.0030000000000000001)) * (1.0029999999999999 ^ 6)) + (250 * (((1.0029999999999999 ^ 6) - 1) / 0.0030000000000000001))) - 175 every month
- 2,135.00 USD
(175 * (((1.0029999999999999 ^ 12) - 1) / 0.0030000000000000001))
An average contribution can misrepresent the path
The worked example deposits USD 100 in each of the first six months and USD 250 in each of the next six. The comparison deposits USD 175 every month. Both contribute the same principal over twelve months. Under the invented positive monthly rate, their ending balances differ because the equal-payment schedule puts more money into the account earlier. A contribution average preserves the total deposited but not its interest exposure. At zero growth the final totals would match, which provides a useful check. This result does not argue against increasing contributions later. It shows that an average monthly amount is an incomplete substitute for an explicitly dated plan whenever growth matters.
Use phase boundaries to diagnose progress
A stepped plan naturally creates checkpoints. At the end of the first phase, compare the actual balance with the planned phase balance and confirm that the later increase is still affordable. If deposits were lower or the expected event changed, solve the remaining target from the current balance rather than preserving the initial average. The checkpoint also reveals whether a shortfall came from contributions, growth, or withdrawals. Those causes call for different responses. A rate adjustment affects the projection, while a contribution adjustment affects household cash flow. Keeping them separate makes the review useful: it identifies the input that actually changed instead of attributing every difference to account yield or to the saver failing to meet an averaged number.
Stress-test the later phase
Investor.gov's compound-growth calculator treats interest as estimated; future contribution increases deserve the same conditional treatment. Construct a scenario where the second-phase amount stays at the original level, and determine the resulting gap or delayed finish date. Another scenario can retain the higher deposits but use zero growth. These are feasibility checks, not probabilities. The table itself uses two fixed schedules to isolate timing, with no charges or interruptions. It does not validate a future income forecast. A practical stepped plan works best when the phase change has a clear date, the contributions fit actual cash availability, and the target is recalculated when that date or capacity changes rather than hidden behind an annual average.
Supporting references: 2. SEC Investor.gov: Compound Interest Calculator
Test another situationA delayed step can be translated into a fixed gap
A separate hypothetical case. Its inputs differ from the main worked example above.
A delayed step can be translated into a fixed gap
Imagine a hypothetical plan with six month-end deposits of USD 100 followed by six of USD 200, with zero growth. The endpoint is USD 1,800. If the larger deposit begins two months late, eight deposits remain USD 100 and only four reach USD 200, producing USD 1,600. The resulting USD 200 gap requires an additional USD 50 on each of those four final dates to preserve the original endpoint. The inputs are invented and the total schedule stays within the same year. The trade-off is a more demanding final phase versus a lower target or a later purchase if the expected improvement in cash capacity is delayed.
Tie the step to a verifiable event
Investor.gov's savings-goal framework makes contributions an explicit input. Record what releases money for the higher phase, such as the actual ending of a contractual payment, and confirm its last payment date. An expected income change should remain conditional until supported. A flat monthly average conceals whether most funding arrives late and whether the step has happened. Review the balance at the phase boundary, then solve the remaining gap using actual dates. If growth is included, the early-phase subtotal also continues earning during the later phase; stopping its accumulation at the boundary understates exposure while assuming every late deposit earns all year overstates it.
Supporting references: 1. SEC Investor.gov: Savings Goal Calculator
Check this case’s calculations
- Original stepped principal
- 1,800.00 USD
((100 * 6) + (200 * 6)) - Delayed-step principal
- 1,600.00 USD
((100 * 8) + (200 * 4)) - Remaining gap
- 200.00 USD
(1800 - 1600) - Final-date catch-up increment
- 50.00 USD per deposit
((1800 - 1600) / 4)
Limits of this additional case
- The catch-up increment assumes the final four higher deposits are affordable; a delayed income increase may invalidate that capacity.
Limits of this analysis
- A planned later income increase may not occur.
- Actual contribution changes may be irregular rather than two equal phases.
- Constant monthly growth and zero fees are illustrative only.
Sources and scope
- SEC Investor.gov: Savings Goal Calculator
A savings target can be analyzed with initial funds, time, and estimated interest.
Scope: US planning tool; independently derived cash-flow examples.. 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
