Help - Periodic Payment for a Future Cash (invest)
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Periodic Payment for a Future Cash
Purpose
This calculator answers a savings-goal question: how much do I need to set aside every period to reach a target amount by a future date, given an expected interest rate? It is useful for planning contributions toward a future goal — such as a down payment, a large purchase, or a sinking fund — when you know the target amount, the rate you expect to earn, and how long you have.
Background
Saving toward a target (a sinking fund)
Instead of starting with a lump sum and letting it grow, this calculator assumes you contribute an equal amount every period, and each contribution earns interest from the time it is made until the target date. It solves for the contribution size that makes the accumulated value — contributions plus the interest they earn — equal exactly the Future Value you want, after the stated Number of Periods.
Inputs
Future Value
The target amount you want to have accumulated by the end of the period.
Interest Rate
The interest rate your contributions are expected to earn, entered with a
time basis (for example, 6.0 pct/yr). It is converted proportionally to
match the time unit of Number of Periods — for example, an annual rate
is divided by 12 to get a monthly rate. This is a simple proportional
conversion, not a compounding conversion, so entering the rate directly in
the same time unit as Number of Periods (for example, a monthly rate
when periods are months) gives the same result and avoids any ambiguity.
Number of Periods
How many equal contribution periods there are until the Future Value
is needed (for example, 12.0 mo). Its time unit also determines how
Interest Rate is converted, as described above.
Results
Payment Per Period
The fixed amount to contribute at the end of every period so that, with interest, the contributions grow to exactly the Future Value by the end of Number of Periods.
Total Payment
Payment Per Period multiplied by Number of Periods — the sum of all contributions before counting the interest they earn. It is always less than the Future Value, with the difference being the interest earned over the periods.
Understanding the Calculation
The interest rate is first expressed as a rate per period matching the time unit of Number of Periods. The required periodic contribution is then:
where is the interest rate per period, is the Future Value, and is the Number of Periods. This is the standard sinking-fund payment formula — the amount whose repeated deposits, compounding each period, exactly reach after periods.
Example
Using the default inputs — a Future Value of 100,000, an Interest Rate of 6.0% per year, and 12.0 months of contributions — the calculator converts 6% per year to 0.5% per month, and returns a Payment Per Period of approximately 8,106.64 (per month) and a Total Payment of approximately 97,279.72. The gap between the Total Payment and the 100,000 Future Value — about 2,720.28 — is the interest earned on the contributions over the year.
Important Assumptions and Interpretation
- Payment Per Period is assumed to be made at the end of each period, a fixed and evenly spaced amount, with no missed or irregular contributions.
- Interest Rate is assumed constant across every period.
- Because the rate conversion to match Number of Periods is a simple proportional split rather than a compounding-equivalent conversion, for the clearest results enter Interest Rate already in the same time unit as Number of Periods (for example, a monthly rate for monthly periods) if you want to avoid any approximation from the conversion step.
- The result is a savings plan estimate based on a constant assumed rate; actual investment returns will vary.