How is the monthly saving needed for a goal calculated?

The monthly amount needed to reach a savings goal depends on four things: the target amount, the time available, the capital already saved, and the return the investments are assumed to earn. The calculation works backwards from the goal, using the formula for the future value of regular payments.

The formula

With a monthly return $i$ , a number of months $n$ , a starting capital $V_0$ and a target $G$ , the starting capital and the monthly contributions $C$ must grow to the target together:

G = V_0 \, (1 + i)^n + C \, \frac{(1 + i)^n - 1}{i}

Solving for the monthly contribution gives:

C = \frac{\left(G - V_0 \, (1 + i)^n\right) \times i}{(1 + i)^n - 1}

A yearly return $r$ corresponds to a monthly return of $i = (1 + r)^{1/12} - 1$ .

A simple illustration

The goal is €200,000 in 20 years, starting with €20,000 and assuming a return of 6% a year — about 0.487% a month:

(1 + i)^{240} \approx 3.207 \qquad V_0 \, (1 + i)^{240} \approx 64{,}140

C = \frac{(200{,}000 - 64{,}140) \times 0.00487}{3.207 - 1} \approx 300

About €300 a month is needed. Of the final €200,000, €72,000 comes from the monthly contributions and €20,000 from the starting capital; the remaining €108,000 comes from returns.

How the inputs change the result

Change from the example	Monthly amount needed
+62,020,000	about €300
+46	about €430
+86	about €190
+2,520	about €170
no starting capital	about €440

Time and return matter as much as the monthly amount: five more years cut the required saving by more than 40%.

Things to keep in mind

Use a realistic return, preferably a real one. Planning in today's money — with a return after inflation — keeps the target meaningful; €200,000 in 20 years will buy much less than €200,000 today.
Returns are not steady. The formula assumes the same return every month. Actual results vary, which is why a Monte Carlo simulation of the probability of reaching the goal is a useful complement.
Costs and taxes reduce the effective return, and should be deducted from the assumption.
Review it regularly. If returns fall short of the assumption, the monthly amount has to rise — and the earlier that is noticed, the smaller the adjustment.

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