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Future Value = PV × (1+r)ⁿ + PMT × [(1+r)ⁿ − 1] / r
where PV = current savings, r = annual return rate ÷ 12 (monthly compounding), n = months to retirement, PMT = monthly contribution.
Annual sustainable income = Final pot × 0.04 (4% rule — Trinity Study, 1998)
Worked example: 50,000 in savings, 500/month contributions, 6% annual return, 25 years to retirement. Future Value ≈ 490,000. Sustainable annual income ≈ 19,600/year. A state pension of 10,000/year would reduce the required pot to cover just 9,600/year, implying a pot target of only 240,000 — dramatically reducing the personal savings required.