EAR Calculator

What this calculator estimates

The calculator produces four linked outputs. The effective annual rate is the true one-year percentage change caused by compounding. The periodic rate is the rate applied at each compounding event. The final balance projects the starting principal through the selected term. The total interest is the final balance minus the initial balance.

EAR isolates the mathematical effect of compounding. It does not automatically include fees, taxes, penalties, variable-rate changes, deposits, withdrawals, or scheduled loan repayments. For consumer borrowing, compare the disclosed APR and product terms as well. The Consumer Financial Protection Bureau’s APR explanation provides useful context.

How the formula works

EAR = (1 + r ÷ m)^m − 1

Here, r is the nominal annual rate written as a decimal and m is the number of compounding periods per year. A 12% nominal rate compounded monthly has a periodic rate of 1%. Reapplying that 1% twelve times gives an EAR of about 12.6825%, not exactly 12%.

For continuous compounding, the limiting formula is EAR = e^r − 1. Future value is calculated from the same growth factor over the selected number of years. The Investor.gov compound interest resource offers a broader view of long-term compounding.

How to enter each input

• Nominal annual interest rate: enter the quoted yearly rate, such as 8% or 12.5%. This field is required. Higher positive rates increase EAR and future value. A common mistake is entering a monthly rate as though it were annual.
• Compounding frequency: choose how often interest is capitalized. Annual means once per year; monthly means twelve times; daily uses an average 365.242-day year; continuous represents the mathematical limit. More frequent compounding generally raises EAR for a positive nominal rate.
• Term in years: enter the projection horizon. It is required and may include decimals. The term changes final balance and total interest but does not change the one-year EAR itself.
• Initial balance: enter the starting principal in dollars. It is required for the balance projection. A larger balance scales dollar interest proportionally but does not alter the percentage rates.

Reset clears the calculator to a neutral zero state. Currency symbols, commas, spaces, and percent signs are accepted when typing.

How to read the results

A positive EAR premium means compounding raises the effective rate above the nominal quote. With annual compounding, nominal rate and EAR are equal. At zero interest, both are zero. For negative rates, EAR may be slightly less negative than the nominal rate depending on frequency, provided the mathematical growth factor remains valid.

The periodic rate helps verify the calculation. For example, 12% nominal compounded monthly equals 1% per month. Continuous compounding has no finite periodic rate, so the result is shown as “Continuous.”

The final balance is the projected principal after the full term, while total interest measures the dollar change. A negative total indicates decline rather than growth. These outputs assume the rate and frequency stay constant throughout the term.

Interpreting the chart and table

The chart holds the nominal rate constant and plots EAR across annual, semi-annual, quarterly, monthly, weekly, daily, and continuous compounding. The curve usually rises quickly at first and then flattens, illustrating diminishing incremental benefit from ever-more-frequent compounding.

The table gives the exact periodic rate, EAR, one-year ending balance, and one-year interest for every frequency. The highlighted row is your current selection. Use it to compare products that quote the same nominal rate under different compounding conventions.

For a concise definition and additional examples, see Investopedia’s effective annual interest rate overview.

Benefits, tradeoffs, and common mistakes

EAR makes rate comparisons more consistent because it translates different compounding schedules to one annual basis. It is particularly helpful for deposits, credit products, bonds, and quoted investment returns. The tradeoff is that EAR is still a simplified rate measure: it does not capture cash-flow timing, fees, taxes, changing rates, or credit risk.

• Do not compare a monthly rate directly with an annual rate without converting both to a common basis.
• Do not assume APR and EAR are interchangeable; disclosure rules and fee treatment may differ.
• Do not project long terms with a constant rate unless that assumption is reasonable.
• Check whether a provider uses 365 days, 365.242 days, 360 days, or another day-count convention.

This calculator is educational and does not provide personalized financial, legal, tax, or investment advice.