Investment Return Formulas
Total return on a lump sum:
FV = PV × (1 + r)^t
PV = initial investment | r = annual return | t = years
CAGR (Compound Annual Growth Rate):
CAGR = (Ending Value ÷ Beginning Value)^(1 ÷ Years) − 1
With annual contributions:
FV = PMT × [(1 + r)^t − 1] ÷ r
PMT = annual contribution (end of year)
New York example — $$12,873/year at 7%:
- After 10 years: $177,859 ($128,730 contributed)
- After 20 years: $527,735 ($257,460 contributed)
- After 30 years: $1,215,994 ($386,190 contributed + $829,804 gains)
Tax note for New York investors: In a taxable brokerage account, investment gains are subject to 10.9% state income tax plus federal capital gains tax (~15% for long-term). Combined rate ≈25.9%, reducing an effective 7% return to approximately 5.2% after tax. Tax-advantaged accounts avoid this drag entirely — use them first.