The reverse formula
Let the target G be measured after n equal periods. The amount already available is P, the rate per period is i, and equal contributions C arrive at the end of each period. Income remains invested, while expenses and taxes are excluded. Then G = P × (1 + i)ⁿ + C × ((1 + i)ⁿ − 1) / i. Therefore C = (G − P × (1 + i)ⁿ) × i / ((1 + i)ⁿ − 1). At a zero rate, use C = (G − P) / n. If the result is negative, the model indicates excess starting funding; it does not require a negative payment.
A calculation with an initial amount
The educational target is 600,000 roubles; 100,000 has already been set aside, and the horizon is 36 equal months. At an assumed rate of 0.5% per month, the required contribution at the end of each month is 12,210.97 roubles. The rate is not a market benchmark. Without income, the monthly amount would be 13,888.89 roubles. If the horizon is extended to 48 months at the same assumed rate, the contribution falls to 8,742.51 roubles. The formula uses high internal precision; the displayed amounts are rounded to kopecks.
These answers show different ways to change a plan: increase the contribution, extend the horizon, reduce the target or increase the amount already set aside. Raising assumed returns also lowers the calculated contribution, but it does not create available money or remove risk. This is a different lever: it changes an assumption about the future, whereas an actual transfer increases own funding. If a required target is reached only in the most optimistic scenario, state that dependence rather than presenting it as a base promise.
Rounding and control
A rounded contribution can produce a small shortfall or surplus at the end of the horizon. After choosing a convenient amount, run a forward table and assess the balance on the required date. A final payment can be marked separately as a corrective element of the educational plan; whether a real top-up may be changed depends on the account terms. Do not round the growth factor to two decimal places at every step. Keep internal precision and show monetary amounts separately. Also check whether contributions are due at the beginning of the month; in that case the contribution formula has an additional factor.
If the contribution does not fit the budget
Compare it not with average income but with money left after mandatory expenses and payments on the relevant dates. State what amount has already been assigned to other goals: one balance cannot be counted as the starting amount for several independent plans at once. For irregular income, model weak months and missed contributions instead of replacing them with an annual average. An unreceived bonus remains a scenario. An already accumulated [emergency fund](/guides/emergency-fund/) does not automatically become a free initial contribution for a purchase.
What to review
Record the next review date, the new target price, actual contributions, the available rate and the remaining horizon. Changing one condition requires a new calculation, not a conclusion that the plan is permanently broken. If expenses are only approximate, show a target range. Do not call an amount sufficiently reliable merely because the formula balances to the kopeck. The mathematical answer is exact within its assumptions; the real-life problem includes uncertain income, access to money and whether the deadline is binding. That boundary makes reverse calculation a planning tool, not a promise of an outcome.
A missed contribution is a new starting point
After a missed payment, it is not always appropriate to divide its amount evenly among the remaining months. The earlier contribution would have earned income for some time, and its absence changes the future base. Use the actual balance, the remaining number of periods and the updated target, then solve the reverse problem again. This keeps the adjustment consistent with the same accrual method. If the compensating contribution exceeds free cash flow, the table should show the constraint. Do not fix it through an undisclosed increase in the scenario rate or by using money already assigned to another mandatory expense.
Convert an annual rate to a periodic rate by checking the material on the [effective rate](/guides/effective-rate/), rather than choosing the unit that produces a convenient contribution.