🎯 Savings Goal Calculator

FV = PV(1+r)^n + PMT × [(1+r)^n - 1] / r PV = Current savings r = Monthly interest rate (APY / 12 / 100) n = Number of months PMT = Monthly contribution FV = Future value (savings balance) If FV = Goal → n is how long it takes

PMT = (Goal - PV(1+r)^n) × r / [(1+r)^n - 1] This tells you exactly how much to save per month to reach your goal in exactly n months, given your current savings and interest rate. Example: Goal $30K, saved $5K, 4.5% APY, 48 months r = 4.5/12/100 = 0.00375 PV = $5,000 n = 48 PMT = ($30,000 - $5,000×1.00375^48) × 0.00375 / (1.00375^48 - 1) PMT ≈ $467/month

n = log[(PMT + FV×r) / (PMT + PV×r)] / log(1+r) Or simply: simulate month by month until balance reaches goal (this calculator uses simulation for accuracy with edge cases). No-interest case (r=0): n = (Goal - Current) / Monthly

Saving $500/month toward $30,000 goal ($5K saved): Rate 0%: 52 months to goal ($0 interest earned) Rate 2%: 50 months ($270 earned) Rate 4.5%: 48 months ($600 earned) Rate 7%: 46 months ($950 earned) Higher-yield savings accounts (HYSA) at 4-5% APY can meaningfully shorten your timeline.