Compound Interest Guide: Growth Over Time
Learn how principal, rate, time, and compounding frequency change future value.
Quick Answer
A = P(1 + r/n)^(nt); interest earned = A − PWhen to Use This
Estimate growth of a starting balance when interest stays invested. Here P is principal, r is a fixed nominal annual rate written as a decimal, n is compounding periods per year, and t is years. The examples assume no deposits, withdrawals, fees or taxes and are hypothetical, not promised returns.
Step-by-Step Method
- Enter the starting principal P.
- Enter the annual rate as a percent in the tool; use its decimal form r in the formula.
- Enter the duration in years t and select compounding frequency n.
- Calculate the future balance A, then subtract P to find interest earned.
Calculator Tips and Limits
- Compare compounding frequencies only while holding the nominal annual rate, term and cash flows fixed.
- APY is already an effective annual yield; it is not interchangeable with a nominal rate without conversion.
Worked Examples
Annual compounding with visible year totals
Start with $1000 at a fixed nominal 5% for 2 years, compounded annually. After year one: 1000 × 1.05 = $1050. After year two: 1050 × 1.05 = $1102.50. Interest is $102.50, compared with $100 under simple interest for the same principal, rate and time.
Changing only the frequency
With monthly compounding, n = 12 and nt = 24. A = 1000 × (1 + 0.05/12)^24 ≈ $1104.94. Interest is about $104.94. This comparison assumes the same nominal annual rate in both cases.
Common Mistakes
Omitting the time period
A rate alone does not determine the final balance. Two years means 24 periods for monthly compounding, not 12.
Treating an estimate as a guaranteed yield
Rates, losses, fees, taxes and cash flows can change real outcomes. Verify the assumptions of the actual account or investment.
FAQ
What if the rate is zero?
Without deposits or withdrawals, the balance remains P. No interest accumulates regardless of compounding frequency.
Does more frequent compounding always prove one product is better?
No. The simple comparison assumes a fixed positive nominal rate and identical terms. Fees, risk, effective yields and withdrawal rules also differ between products.
References and corrections
Investor.gov: Compound Interest Calculator. The worked examples on this page are CalcSolver explanations. Read our calculation and correction method, or report an error with the input and expected result.