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Future value of lump sum: FV = PV × (1 + r)ⁿ
Future value of regular contributions: FV = PMT × [(1 + r)ⁿ − 1] ÷ r
Combine both formulas for an initial deposit plus regular contributions.
Worked example: 10,000 initial deposit + 500/month contributions, 7% annual return, 20 years. Lump sum FV = 10,000 × 1.07²⁰ ≈ 38,697. Monthly contributions FV ≈ 262,000 (with monthly compounding). Combined ≈ 300,000. Total contributions: 10,000 + (500 × 240) = 130,000. Investment return generated: approximately 170,000.