What compound interest means
When interest compounds, each period adds to the balance that earns interest next period. Small rate differences become large wealth differences over decades because growth accelerates rather than staying perfectly linear.
The core formula (lump sum)
For a single deposit P at annual rate r expressed as a decimal, compounded n times per year for t years: A = P·(1 + r/n)^(n·t). Monthly contributions need the annuity form your calculator implements—always align n with how often interest credits.
Worked example
$10,000 at 6% annual compounded monthly for 10 years: use r = 0.06, n = 12, t = 10. The ending balance is higher than simple interest because monthly compounding credits gains earlier inside the year.
APR vs APY
APR quotes the nominal yearly rate; APY reflects compounding. Two accounts can advertise similar APR but different APY if compounding cadence differs. Your calculator inputs should match the bank’s compounding schedule.
Common pitfalls
Mixing monthly deposits with annual rates without converting periods is the top error. Another is treating quoted rates as continuous when they are discrete monthly. Always verify whether “rate” is nominal annual or effective annual.