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 Jersey example — $$15,644/year at 7%:
- After 10 years: $216,145 ($156,440 contributed)
- After 20 years: $641,333 ($312,880 contributed)
- After 30 years: $1,477,745 ($469,320 contributed + $1,008,425 gains)
Tax note for New Jersey investors: In a taxable brokerage account, investment gains are subject to 10.75% state income tax plus federal capital gains tax (~15% for long-term). Combined rate ≈25.75%, reducing an effective 7% return to approximately 5.2% after tax. Tax-advantaged accounts avoid this drag entirely — use them first.