Compound Interest Calculator
Free compound interest calculator with APY, daily/monthly/continuous compounding, recurring contributions, doubling time, and inflation-adjusted view.
Frequently asked questions
What is the compound interest formula?
For discrete compounding: A = P·(1 + r/n)^(n·t), where P is principal, r is the annual interest rate, n is the number of compounding periods per year, and t is time in years. For continuous compounding it becomes A = P·e^(r·t). When recurring contributions are added, the future-value annuity factor PMT·((1+r/n)^(n·t) − 1)/(r/n) is added to the compound principal balance.
What is the difference between APR and APY?
APR (Annual Percentage Rate) is the stated nominal rate before compounding. APY (Annual Percentage Yield) is the effective rate after compounding is applied — APY = (1 + APR/n)^n − 1. A 6% APR compounded daily gives an APY of 6.183%, so APY is always the honest comparison metric between accounts with different compounding schedules.
Does compounding frequency really matter?
For deposit accounts the difference between monthly and daily compounding is tiny — at 6% you go from 6.168% APY to 6.183% APY, roughly $150 on a $100k balance over 10 years. The bigger swing is between annual and continuous. Frequency matters most on debts (credit cards typically compound daily) and on long investment horizons where small APY differences compound into large dollar gaps.
How long does it take to double my money?
Use the Rule of 72: doubling years ≈ 72 / APY (in percent). At 6% APY money doubles in about 12 years, at 8% in 9 years, at 10% in 7.2 years. The exact formula is ln(2) / ln(1 + APY), which this calculator shows in the summary.
What is continuous compounding?
Continuous compounding is the theoretical limit where interest accrues every instant, using A = P·e^(r·t). It sets the upper bound on how much a stated rate can earn with any compounding schedule. In practice banks use daily or monthly compounding, which produce results within a few basis points of continuous.
Should I compare accounts on interest rate or APY?
Always compare on APY. A 5.10% APY account beats a 5.15% stated rate that compounds annually (5.15% APY), even though the stated rate is higher. Federal regulation requires deposit accounts to disclose APY exactly so consumers can make apples-to-apples comparisons.