EAR Calculator

Nominal interest rates can be misleading because they often ignore compounding frequency. The EAR corrects this by calculating the annualized rate of interest under the assumption that interest is compounded periodically. The primary formula used is EAR = (1 + i / n)^n - 1, where i represents the nominal annual interest rate and n represents the compounding frequency per year. For continuous compounding, the formula shifts to EAR = e^i - 1, utilizing Euler's number to determine growth at every possible infinitesimal moment.

Imagine you deposit an initial balance of $10,000 into a high-yield savings account offering a nominal interest rate of 6% (0.06), compounded monthly. This means the compounding frequency (n) is 12. To find the Effective Annual Rate, we divide the nominal rate by the frequency to find the periodic interest rate: 6% / 12 = 0.5% per month. Next, we apply the EAR formula: EAR = (1 + 0.06 / 12)^12 - 1, which simplifies to (1.005)^12 - 1. Evaluating this gives approximately 0.06167, meaning your true Effective Annual Rate is 6.17%. Over the course of one year, your final balance will grow to $10,616.78, outperforming the nominal 6% expectation due to the power of monthly compounding.

Always verify whether your quoted interest rate is nominal or effective before signing a loan or opening a deposit account. When comparing multiple financial products, ensure you compare their respective EARs rather than nominal rates, as a product with more frequent compounding will yield higher returns or costs. Pay close attention to the compounding frequency parameter, as daily or continuous compounding yields notably higher effective rates over multi-year horizons compared to annual compounding.