Introduction
Compound interest applies growth not only to the original principal but also to interest accumulated in earlier periods. This creates growth on growth over time.
The formula is useful for educational savings projections, but actual returns, fees, taxes and rates can produce different outcomes.
Key concept
The standard formula is A = P(1 + r/n)^(nt), where P is principal, r is the annual rate as a decimal, n is the number of compounding periods per year, t is time in years and A is the estimated ending amount.
Formula example
For $1,000 at 5% compounded annually for two years, A = 1,000 × (1 + 0.05)^2 = $1,102.50. The estimated compound interest is $102.50.
Regular contributions require an additional future-value calculation because each deposit has a different amount of time to grow.
Common mistakes
Enter 5% as 0.05 inside a formula, keep the time unit consistent with the compounding period and do not assume that a stated annual rate guarantees a return.
Comparing projections also requires consistent assumptions about contribution timing, fees and compounding frequency.
Interpreting the result
Treat the result as a mathematical projection based on the values entered. Testing several rates and time periods can show how sensitive the estimate is to its assumptions.