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)
Massachusetts example — $$15,724/year at 7%:
- After 10 years: $217,250 ($157,240 contributed)
- After 20 years: $644,613 ($314,480 contributed)
- After 30 years: $1,485,301 ($471,720 contributed + $1,013,581 gains)
Tax note for Massachusetts investors: In a taxable brokerage account, investment gains are subject to 5% state income tax plus federal capital gains tax (~15% for long-term). Combined rate ≈20%, reducing an effective 7% return to approximately 5.6% after tax. Tax-advantaged accounts avoid this drag entirely — use them first.