EAR Calculator

How to use this calculator

Two required inputs. Two optional inputs that activate the balance and earnings outputs.

Nominal Interest Rate (%) is the stated rate — the number printed on the savings account disclosure, bond prospectus, or loan agreement before compounding is applied. This is the APR. Do not enter an APY here.

Compounding Frequency is how often the lender or institution applies interest within a year. Select from Daily (365 times), Weekly (52 times), Monthly (12 times), Quarterly (4 times), Semi-annually (twice), Annually (once), or Continuously (mathematical limit). If you are unsure which frequency your account uses, check the account agreement or call your bank.

Principal (optional) adds a dollar figure to the calculation. If entered, the calculator shows your actual balance and interest earned after the specified time period.

Time Period in years (optional) works together with the principal. Set it to 1 for a one-year projection, 5 for five years, and so on. You can use decimals: 0.5 for six months.

The comparison table at the bottom is generated automatically for any nominal rate you enter — it shows EAR across all seven compounding frequencies side by side. The currently selected frequency is highlighted.

What EAR actually measures

The Effective Annual Rate (EAR) is the actual annualized rate of interest after accounting for how often it is compounded within a year. It is the true cost of borrowing and the true return on saving.

APR (Annual Percentage Rate) is the nominal rate. It is stated before compounding is applied. When a bank says your savings account earns 5% APR compounded monthly, the 5% is the nominal rate. What you actually earn is slightly more — the EAR.

EAR and APY (Annual Percentage Yield) are the same concept. Regulations in the US require banks to display APY on deposit accounts so consumers can make meaningful comparisons. EAR is used in academic and analytical contexts; APY is the consumer-facing version.

The distinction matters enormously when comparing financial products. Two savings accounts both advertising “5% interest” can have different real returns if one compounds monthly and the other compounds quarterly. Two loans both quoted at “8% APR” can have different true costs depending on compounding schedules. EAR makes the comparison fair.

The formula

For standard compounding (any finite frequency):

EAR = (1 + r/n)^n - 1

Where:

• r = nominal annual rate as a decimal
• n = number of compounding periods per year

For continuous compounding (the mathematical limit as n approaches infinity):

EAR = e^r - 1

Where e is Euler’s number, approximately 2.71828.

From EAR, the effective daily rate is:

Daily Rate = (1 + EAR)^(1/365) - 1

And the effective rate for any arbitrary period of t years:

Return = (1 + EAR)^t - 1

How compounding frequency changes EAR: a full comparison

This table shows EAR at three common nominal rates across all major compounding frequencies. The pattern is clear: higher nominal rates amplify the impact of compounding frequency.

Compounding Frequency	Periods/Year	EAR at 6%	EAR at 12%	EAR at 20%
Annually	1	6.0000%	12.0000%	20.0000%
Semi-annually	2	6.0900%	12.3600%	21.0000%
Quarterly	4	6.1364%	12.5509%	21.5506%
Monthly	12	6.1678%	12.6825%	21.9391%
Weekly	52	6.1800%	12.7341%	22.0934%
Daily	365	6.1831%	12.7475%	22.1336%
Continuously	inf	6.1837%	12.7497%	22.1403%

Notice that the gap between monthly and daily compounding at 6% is only 0.0153 percentage points. The same gap at 20% is 0.1945 percentage points. High-rate debt (credit cards, payday loans) is where compounding frequency has a genuinely material impact on the total cost.

EAR in practice: where it matters most

Savings accounts and CDs. Federal Regulation DD requires US banks to disclose APY, which is EAR by another name. When you see “4.75% APY” on a high-yield savings account, that is already the effective rate after daily compounding. No conversion needed.

Credit cards. This is where EAR stings. A credit card with a 24% APR compounded daily has an EAR of 27.11%. If you carry a $5,000 balance for a full year without paying, you will owe approximately $1,355 in interest — not $1,200 as the nominal 24% would suggest.

Mortgages and auto loans. US mortgages are typically quoted as APR and compound monthly. A 7% APR mortgage has an EAR of 7.229%. On a 30-year loan of $300,000, this difference compounds into a meaningful additional cost over the life of the loan.

Corporate bonds. Many bonds pay semi-annual coupons. A 6% coupon bond compounding semi-annually has an EAR of 6.09%. When comparing to a corporate bond with monthly coupon payments at the same 6% nominal rate (EAR 6.168%), the monthly-paying bond offers a slightly higher effective return.

Continuous compounding: the theoretical maximum

Continuous compounding is the limiting case as compounding frequency approaches infinity. In practice, no financial product actually compounds continuously, but the concept matters in financial mathematics and options pricing.

The formula for continuous compounding comes from the limit of (1 + r/n)^n as n goes to infinity, which converges to e^r. The number e (Euler’s number, approximately 2.71828) appears naturally as the base of the natural logarithm and is central to exponential growth mathematics.

Common mistakes when working with EAR

Entering APY as the nominal rate. If your savings account shows 5.12% APY and you enter that as the nominal rate for monthly compounding, the calculator will show you a higher EAR than 5.12%, which is double-counting the compounding effect. The APY is already the EAR — no further conversion is needed.

Ignoring compounding when comparing loans. Two personal loan offers at 10% APR with different compounding frequencies have different effective costs. Monthly compounding (EAR 10.471%) costs more than quarterly compounding (EAR 10.381%) on the same nominal rate.

Assuming EAR fully captures credit card costs. EAR applies to the balance outstanding. If you carry different balances each month (because you are making payments and adding new charges), the actual interest cost is harder to calculate from EAR alone. The total interest figure from a payoff calculator is more useful for credit card analysis.

Forgetting that EAR applies to fees too. Some financial products have annual fees or periodic charges that are not reflected in the stated APR. A 0% APR credit card with a 2% annual fee has a real cost. Adding fees to the total cost calculation gives a more accurate picture than EAR alone.

Bottom line

EAR is the correct rate to use when comparing any two financial products with different compounding schedules. The nominal APR is useful for quick reference but misleads whenever compounding frequency differs between options.

For savers, always look at APY rather than APR when comparing accounts. For borrowers, understand that a lower APR with more frequent compounding can cost more than a higher APR with less frequent compounding. The comparison table this calculator generates instantly shows this relationship for any nominal rate you enter.

The practical upshot: for typical savings rates (under 10%), the difference between monthly and daily compounding is tiny — under 0.02 percentage points. For high-interest debt (20-30% APR), the compounding premium is substantial enough to materially change the true cost. This is one reason high-rate debt is so damaging and why its effective cost is often higher than borrowers realize from the stated APR alone.