How this accumulation model works
For y years, n = 12y, effective annual return g and month-end contribution C, i = (1 + g)^(1/12) − 1 and FV = P(1 + i)^n + C × ((1 + i)^n − 1)/i. At zero return, FV = P + nC. Rates in these formulas are decimals.
Your target T is entered in today’s money. Its future nominal value is T × (1 + inflation)^y; the planned balance in today’s purchasing power is FV divided by the same factor. Required total monthly contribution uses the same month-end model with that nominal target, returning zero when the principal alone is sufficient at the end date. For a zero-year span, no monthly amount is solved.
Illustrative example: current age 30, retirement age 31, current savings 0, monthly contribution 500, return 0%, inflation 0% and today’s target 12,000. The planned balance is 6,000, the balance-minus-target difference is −6,000, required total monthly contribution is 1,000 and additional monthly contribution is 500. Currency selection changes display only.
Hypothetical educational calculations, not financial advice or predictions. This model only accumulates savings to a chosen age. It does not calculate retirement success probability, spendable income or withdrawals; it excludes Social Security, pensions, Roth IRA/401(k) rules, contribution limits, fees and taxes. It does not recommend an age, savings rate or investment return.