Find the monthly contribution required to hit a savings target.
Future-value-of-annuity: pmt = (target − starter·(1+r)^n) / ((1+r)^n − 1)·r, with r = APR/12 and n = months. Returns are not guaranteed; the rate is an expectation, not a contract.
Most savings advice is framed as "save X € / month" without telling you whether X gets you to your actual goal. The reverse problem — here is the goal, the horizon, and the expected return; what monthly contribution gets me there? — is a future-value-of-an-annuity solve. Doing it on paper is fiddly because compounding interacts with the contribution stream. People typically overestimate or underestimate by 20–40 % when they guess. A small change in the assumed return (4 % vs 6 % vs 8 %) compounds to large differences over a 10–20-year horizon; the calculator makes that sensitivity visible by re-computing live as you change inputs.
Two parts: (a) the existing starter balance grows on its own at rate r per period for n periods: starter × (1 + r)^n. (b) The contribution stream funds the rest. Future value of an ordinary annuity of pmt per period: pmt × ((1 + r)^n − 1) / r. Setting that sum equal to the target and solving for pmt: pmt = (target − starter × (1 + r)^n) × r / ((1 + r)^n − 1). For r = 0 (no growth, money in a checking account), pmt collapses to (target − starter) / n. The calc uses r = APR / 12 and n = years × 12, so pmt is monthly. If the starter alone grows past the target — say you have 50 k €, want 60 k € in 10 years at 6 % expected — pmt is set to 0 and a note explains "no new contributions needed".
Enter the target amount, your current savings (starter, can be 0), the horizon in years, and the expected annual return. The calc returns the required monthly contribution as the headline KPI, plus diagnostics: total contributed across the horizon, interest earned (the part you didn't have to save), what your starter alone grows into, and what share of the goal that growth represents. If your assumption is "0 % return — just stuff money in a sock", set the return to 0 and the calc gracefully falls back to linear arithmetic.
House deposit: target 30 000 €, current 5 000 €, 5 years, expected 3 % annual return. - Monthly r = 0.03 / 12 = 0.0025. n = 60. - Starter grows: 5 000 × 1.0025^60 ≈ 5 808 €. - Annuity factor: (1.0025^60 − 1) / 0.0025 ≈ 64.65. - pmt = (30 000 − 5 808) / 64.65 = 374.20 €/month. - Total contributed: 374.20 × 60 = 22 452 €. Interest earned: 30 000 − 5 000 − 22 452 = 2 548 €. - Starter share of goal: 5 808 / 30 000 = 19.4 %.
Confusing nominal and real returns. A 6 % nominal return at 3 % inflation is a 3 % real return. If your goal is in today's purchasing power (e.g., "I want 100 k € in 2046 worth of something I can buy now"), use the real return, not the nominal. Most retail savings products advertise nominal — read carefully.
Returns aren't guaranteed. The future-value formula assumes a constant rate. Real markets have drawdowns: the S&P 500's nominal long-run real return is around 7 %, but with sequence risk a 5-year window can be flat or negative. Treat the rate as an expectation, not a contract. For high-confidence goals (a fixed-date purchase), use a near-zero rate and over-contribute, then move to growth assets only the surplus.
Tax drag and fees. The calc gives a pre-tax, pre-fee result. A 6 % return inside a tax-advantaged wrapper (401k, ISA, PEA in France) is genuinely 6 %; outside one, after 30 % capital-gains tax, it's an effective 4.2 %. Subtract realistic fees (0.2–1 % for index funds, 1.5–3 % for actively managed) and the effective rate drops further.
Contributions at start vs end of period. The annuity factor used here is for end-of-period contributions ("ordinary annuity"). Contributing at the beginning of each month (annuity due) adds one extra period of growth — about (1 + r) ≈ 0.5 % more on a 6 % yearly assumption. Negligible at small scales, meaningful for retirement contributions over 30 years.
Currency. Inputs and the result inherit the site's currency-symbol auto-detect; the formula itself is currency-agnostic.