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)
Delaware example — $$13,130/year at 7%:
- After 10 years: $181,410 ($131,300 contributed)
- After 20 years: $538,271 ($262,600 contributed)
- After 30 years: $1,240,270 ($393,900 contributed + $846,370 gains)
Tax note for Delaware investors: In a taxable brokerage account, investment gains are subject to 6.6% state income tax plus federal capital gains tax (~15% for long-term). Combined rate ≈21.6%, reducing an effective 7% return to approximately 5.5% after tax. Tax-advantaged accounts avoid this drag entirely — use them first.