Savings & financial mathematics
Variable Savings Rates: Multiply the Path Instead of Averaging It
Model savings through changing rates, distinguish a compounded path from an arithmetic average, and separate rate effects from contribution timing.
Free financial tools
Bill & payday savings planner
Work out what to set aside at each usable payday before a known bill is collected. Use a contribution count, without assuming a whole year or investment returns.
02 / The result
Your scenario, calculated
Showing the editable example above. Modeled values, not a forecast.
- Regular contribution
- 150.00USD
- Final contribution
- 150.00USD
- Still to fund
- 900.00USD
- Reserved after the plan
- 1,200.00USD
Use the answer for a real decision
Set aside USD 150.00 at each usable contribution, adjusting the last to USD 150.00. Count only transfers that clear before the collection date. Compare this contribution with your available cash; the calculation cannot create the required surplus or move a due date. If no contributions remain, the unfunded amount is needed now.
Before interpreting the result
What this model includes
This is a zero-interest allocation plan, not an investment projection. Count only contributions that can clear before the collection date. A contribution after the bill is collected cannot fund it. The bill amount and money reserved stay fixed; fees, taxes or price changes must be included in the entered bill amount. Existing earmarks are not available to two different bills.
Formula & method
Unfunded bill = max(0, bill amount − money already reserved). Regular contribution = unfunded bill / usable contributions, rounded up to cents. Reduce the final contribution to avoid overfunding.
Background reading: CFPB: saving for a goal and cash-flow timing. These references explain the concepts; they do not endorse this calculator.
03 / Visual evidence
The scenario over time
Vertical scale: USD. Horizontal scale: Contribution. Lines join the calculated points; no probability is implied.
- Reserved balance
- Bill target
Shared value scale; zero is included. These are modeled scenarios using your assumptions, not observed market data. The table provides every plotted value.
Scenario data
USD amounts are displayed to two decimal places. Calculations use unrounded internal values. Scroll across a wide table on smaller screens.
| Contribution | Reserved balance (USD) | Bill target (USD) | This contribution (USD) |
|---|---|---|---|
| 0 | 300.00 | 1,200.00 | 0.00 |
| 1 | 450.00 | 1,200.00 | 150.00 |
| 2 | 600.00 | 1,200.00 | 150.00 |
| 3 | 750.00 | 1,200.00 | 150.00 |
| 4 | 900.00 | 1,200.00 | 150.00 |
| 5 | 1,050.00 | 1,200.00 | 150.00 |
| 6 | 1,200.00 | 1,200.00 | 150.00 |
Try another perspective
Change one assumption at a time, then compare the result. A scenario is a way to examine a decision, not a promise of an outcome.
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Further reading
Savings & financial mathematics
Real Savings Returns: Divide Growth by the Price Change
Calculate the exact inflation-adjusted return, see why subtracting inflation is an approximation, and distinguish account growth from purchasing power.
Savings & financial mathematics
Present Value of Equal Future Payments as a Savings Mathematics Exercise
Value a fixed payment stream by discounting each date, distinguish a mathematical annuity from insurance, and avoid relying on a simple payment total.