Workspace
The calculator's own fields, action and results arrive with the verified pack when you load it. Nothing is computed in this page.
Deposit schedules · solved for the deposit
Required recurring deposit for a target fund
The level deposit per period that builds a chosen fund from an empty account — the sinking-fund payment, from the target amount, annual rate, cadence and deposit count.
Verified engine
What the engine returns
The output is the identical deposit that, made on every scheduled date without exception, lands the fund exactly on the target at the final deposit. Sum those deposits and they come to less than the goal — the remainder is the interest’s contribution, earned in the gaps between the deposits.
Inputs the result is built from
Target fund
Annual interest rate
Deposit and compounding cadence
Total number of deposits
How the result is derived
MethodThe target multiplied by the per-period rate, divided by the annuity accumulation factor over the deposit count — the recurring-deposit future-value closed form rearranged for the deposit; the per-period rate comes from the annual rate split by the cadence.
StandardSinking-fund payment form of the ordinary annuity
GuardAn annual rate at or below zero is refused: the closed form divides by the per-period rate, and the pack declares this refusal among its vectors. With no interest, the deposit is the target split evenly across the count — plain division, not an annuity problem.
Where the deposits stop and the interest takes over
The formula here is the recurring-deposit accumulation read backwards. Where its companion page grows a known deposit into an unknown balance, this one fixes the balance and lets the accumulation factor determine the deposit. There is no starting-balance input to lean on: the schedule of deposits, and the interest it earns, must carry the whole fund.
Multiply the required deposit by the number of deposits and the product falls short of the target. That shortfall is not an error — it is the interest’s share of the fund, the part the schedule earns rather than pays in. The pack’s vectors show it plainly: the deposits sum to less than the goal in every declared case, with the gap widest when the schedule is long or the rate generous.
Time on this page is a count of deposits at a chosen cadence, not a horizon in years. The annual rate is split across the year by that cadence, and each deposit is assumed to land exactly when interest credits, at the end of its period. A monthly schedule and a quarterly schedule toward the same target are different problems with different answers, and the pack’s vectors carry both.
The pack also declares a reverse reading of this same relation: fix the deposit you can actually manage, and solve for how many deposits the fund takes. That is the third arrangement of one equation — balance, deposit, count — and it is often the honest one, since a deposit is a budget fact while a count is merely patience.
The target multiplied by the per-period rate, divided by the annuity accumulation factor over the deposit count — the recurring-deposit future-value closed form rearranged for the deposit; the per-period rate comes from the annual rate split by the cadence.
When this calculation is used
- Sizing the level deposit for a sinking fund — an obligation of known size due after a known number of deposits.
- Turning a target fund into a per-paycheck or per-quarter figure on the schedule the account actually credits.
- Splitting a target into the share the deposits must carry and the share the interest will contribute.
- Flipping the question when the deposit is fixed by budget: how many deposits the same target takes at that amount.
Worked example
A round target due after some years of monthly deposits into an empty account paying an ordinary annual rate.
The output is the identical deposit that, made on every scheduled date without exception, lands the fund exactly on the target at the final deposit. Sum those deposits and they come to less than the goal — the remainder is the interest’s contribution, earned in the gaps between the deposits.
Then let the pack’s declared reverse workflow move the unknown: hold the deposit at what the budget allows, and the same relation returns the count of deposits the target needs instead. Both directions are exercised by the signed pack’s own vectors, and every figure shown is computed by the verified engine after the page loads — none is written into the page.
What each input represents
Target fund
The balance the schedule must reach by the final deposit, stated as the amount on that day. It must be positive — the sinking-fund question only exists when there is a fund to sink toward.
Annual interest rate
The yearly rate the account pays, as a percentage, before tax. The cadence splits it into the per-period rate that decides how much of the target the interest will carry on the deposits’ behalf.
Deposit and compounding cadence
How many times per year deposits land and interest credits, the two sharing one schedule. Optional, defaulting to the monthly cadence.
Total number of deposits
How many deposits the schedule allows before the fund is due — the page’s measure of time. More deposits shrink the required amount twice over: more payments in, and more periods for interest to help.
Assumptions and limits
- The account starts empty; a fund with existing savings behind it is a different calculation with a smaller answer.
- Deposits are identical and land at the end of each period, on the same schedule the interest credits.
- The rate is constant across the entire schedule and stated before tax.
- Every scheduled deposit is made — the arithmetic has no mechanism for catching up a missed one.
- The target is the nominal amount due on the final date, with any inflation adjustment made before it is entered.
What the guards protect against
- An annual rate at or below zero is refused: the closed form divides by the per-period rate, and the pack declares this refusal among its vectors. With no interest, the deposit is the target split evenly across the count — plain division, not an annuity problem.
- A target at or below zero is refused. A fund of nothing needs no schedule, and a negative target is not a saving question.
- The deposit count and cadence are bounded to schedules an account could really run, from annual up to daily, so every answer describes a possible plan.
Provenance
Sinking-fund payment form of the ordinary annuity
The target multiplied by the per-period rate, divided by the annuity accumulation factor over the deposit count — the recurring-deposit future-value closed form rearranged for the deposit; the per-period rate comes from the annual rate split by the cadence.
An educational reference on sinking-fund arithmetic — not financial advice, and no account’s actual terms are assumed. The signed pack carries its own citation; the page reports the verification state of the release it mounted rather than asserting one.