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)
Montana example — $$11,301/year at 7%:
- After 10 years: $156,140 ($113,010 contributed)
- After 20 years: $463,290 ($226,020 contributed)
- After 30 years: $1,067,501 ($339,030 contributed + $728,471 gains)
Tax note for Montana investors: In a taxable brokerage account, investment gains are subject to 5.65% state income tax plus federal capital gains tax (~15% for long-term). Combined rate ≈20.65%, reducing an effective 7% return to approximately 5.6% after tax. Tax-advantaged accounts avoid this drag entirely — use them first.