How the savings goal model works
Let P be starting balance, T the future nominal target, n = years × 12, and g your effective annual return as a decimal. Monthly rate i = (1 + g)^(1/12) − 1. With a month-end contribution C, future balance is P(1 + i)^n + C × ((1 + i)^n − 1) / i. For nonzero i, solve C = (T − P(1 + i)^n) × i / ((1 + i)^n − 1). At zero return, C = (T − P) / n.
If the starting balance alone grows to at least the target at the chosen end date, C is zero. Otherwise the solved contribution is rounded up to 0.01 and that same amount drives all balances and total contributions. Existing balances grow before each month-end deposit. Total contributed = P + nC; hypothetical growth or loss = final balance − total contributed. This solves a monthly contribution, not a required starting lump sum.
Worked illustration: starting balance 0, future target 12,000, one year, and 0% return gives 1,000 per month, total contributions of 12,000, and no growth. With a target of 100 over 12 months at 0%, the exact monthly amount is 100 / 12; rounding up gives 8.34 and a projected final balance of 100.08. The yearly table uses 8.34, not the unrounded amount.
Educational fixed-return model only, not financial advice or a guarantee of reaching a target. The target is nominal at the future date; inflation is not added automatically. No recommended budget ratios, savings products, return rates, tax-adjusted income, taxes, fees, or market volatility. A starting balance above today’s target can still require contributions if a negative return leaves it below the target at the end.