The Compound Interest Formula
For a lump sum with no additional contributions:
A = P × (1 + r/n)^(n×t)
P = principal | r = annual rate | n = compounds per year | t = years
With regular contributions (PMT per compounding period):
A = P × (1 + r/n)^(nt) + PMT × [((1 + r/n)^(nt) − 1) / (r/n)]
Wyoming example — saving $$629/month (10% of median income) at 7% compounded monthly:
- Monthly rate: 7% ÷ 12 = 0.5833%
- After 10 years: $108,870 ( $75,480 contributed + $33,390 interest)
- After 20 years: $327,663
- After 30 years: $767,362 ( $226,440 contributed + $540,922 interest)
The $10,000 lump sum comparison: $10,000 invested at 7% (monthly compounding) for 30 years grows to $81,165 — a 712% total return on the original principal. This is the power of compound interest: returns on returns, compounding continuously over time.