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)]
Washington example — saving $$828/month (10% of median income) at 7% compounded monthly:
- Monthly rate: 7% ÷ 12 = 0.5833%
- After 10 years: $143,314 ( $99,360 contributed + $43,954 interest)
- After 20 years: $431,327
- After 30 years: $1,010,136 ( $298,080 contributed + $712,056 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.