Effective Annual Rate (EAR) Calculator

What the effective annual rate calculator works out

The headline rate on a financial product is almost always nominal — it describes an annual rate but says nothing about when interest is actually credited. If capitalisation happens more than once a year, interest from the early periods starts earning in its own right and the actual outcome for the year exceeds the quoted figure. The effective annual rate (EAR) expresses precisely that actual outcome.

Use the calculator when comparing deposits with different capitalisation frequencies, when assessing the true cost of a credit card or overdraft charged monthly, when converting a monthly or quarterly rate into an annual one, or when checking whether a savings product\'s quoted yield is nominal or already effective. It is the standard way to bring products onto a common basis when their terms are otherwise not directly comparable.

The formula explained in words

EAR = (1 + r/n)^n − 1

• r — nominal annual rate as a decimal. 6% means 0.06.
• n — capitalisations per year: 365 for daily, 12 for monthly, 4 for quarterly, 2 for semi-annual, 1 for annual.
• r/n is the interest credited in a single period. At 6% nominal with monthly capitalisation that is 0.5% a month.

The formula effectively tracks what happens to one unit of currency over a year: each period it grows by r/n, and that growth compounds n times. At n = 1 the effective rate equals the nominal rate. As n rises the result increases, but at a decreasing pace, approaching a ceiling — continuous compounding, calculated as e^r − 1, which at 6% gives 6.1837%.

The formula also runs in reverse. If you know the effective rate you want to achieve, the nominal rate with n capitalisations is n · ((1 + EAR)^(1/n) − 1). An effective 6% with monthly capitalisation requires a nominal rate of 5.8411%.

A worked example

A nominal annual rate of 6% produces the following effective rates depending on capitalisation frequency:

The monthly case step by step: r/n = 0.06 ÷ 12 = 0.005; (1 + 0.005)^12 = 1.061678; subtract one to get 0.061678, or 6.1678%. On €10,000 that means €616.78 of interest for the year instead of €600.00 with annual capitalisation.

Comparing two deposit offers. Bank A offers 3.90% with monthly capitalisation; Bank B offers 3.95% with annual. The headline rate points to B, but A\'s effective rate is (1 + 0.039/12)^12 − 1 = 3.9705% against B\'s 3.9500%. On €20,000 over one year: €794.09 from A versus €790.00 from B. The lower nominal rate wins on the strength of more frequent capitalisation.

The same effect on debt. A credit card quoted at 18% a year and charged monthly costs an effective (1 + 0.18/12)^12 − 1 = 19.56%. On borrowings the effective rate is always above the nominal one, which is exactly why disclosure of it is required.

Practical guidance and the Bulgarian context

For credit, the principal comparison figure under Bulgarian law is not EAR but the annual percentage rate of charge (APRC). The distinction is material: EAR captures only capitalisation frequency, whereas APRC also includes every mandatory cost of the loan — arrangement and servicing fees, commissions, and insurance where it is a condition of approval. That is why the APRC on a consumer loan is often well above the interest rate, while on a fee-free loan the two converge. For deposits, the corresponding disclosure is the annual percentage yield, calculated on the same logic as EAR.

Watch two practical details. First, many offers quote a rate for the term rather than per year — "2% over 6 months" is not 2% a year but roughly 4.04% effective annually. Second, with promotional terms the effective rate for the first year differs from later years; calculate both before committing to a long tie-in.

On tax: individual income in Bulgaria is generally taxed at a flat 10%, while interest on bank deposits carries a final withholding tax whose current rate is worth verifying against the Personal Income Taxes Act in force. For a fair comparison, work out the effective rate after tax as well — that is the number you actually receive.

Limitations of the calculation

The calculator assumes a fixed nominal rate and even capitalisation throughout the year. Fees, commissions, insurance and taxes are excluded — for the full cost of credit use the APRC rather than EAR.

The calculation assumes interest stays in the account until year end. If you withdraw it after every capitalisation, the effective rate is never realised and your actual yield converges on the nominal one. By the same token, deposits closed early often attract a penalty rate that makes the calculation moot.

Finally, EAR is a one-year measure. For multi-year comparisons of realised performance use CAGR, and for irregular contributions and withdrawals use XIRR. Inflation is also outside its scope: for a real return, set the EAR against inflation using the Fisher formula.