What is Effective Annual Rate?
Effective annual rate (EAR) is the actual yearly interest rate when compounding occurs multiple times per year. A bank may advertise a 12% annual rate, but if interest compounds monthly, you're not paying exactly 12%—you're paying more because each monthly addition of interest then earns interest itself.
Consider a practical example: a savings account earning 6% nominally, compounded quarterly. Each quarter, you earn 1.5% (6% ÷ 4), and that earned interest immediately starts earning its own return. By year's end, your effective rate exceeds 6%. The more frequently interest compounds, the greater this gap between nominal and effective rates.
EAR matters most when:
- Comparing loan offers with different compounding frequencies
- Evaluating investment returns across different products
- Understanding the true cost of credit card debt (often daily compounding)
- Assessing savings accounts with various compounding schedules
Calculating Effective Annual Rate
Two formulas determine EAR depending on the compounding method. For standard periodic compounding, use the first equation. For continuous compounding (rare but found in some bonds and derivatives), use the exponential formula.
EAR = (1 + r/m)^m − 1
EAR (continuous) = e^r − 1
r— Nominal annual interest rate (the stated percentage)m— Compounding frequency (how many times per year interest is calculated)e— Euler's number, approximately 2.71828
Real-World Application: Choosing Between Loans
Suppose you're choosing between two £10,000 loans. Option A charges 12% compounded monthly; Option B charges 11.9% compounded daily. Which is cheaper?
Loan A: EAR = (1 + 0.12/12)^12 − 1 = 0.1268 or 12.68%
Loan B: EAR = (1 + 0.119/365)^365 − 1 ≈ 0.1263 or 12.63%
Option B is marginally better, but only by comparing EARs can you see this. The nominal rates alone (12% vs. 11.9%) don't reveal the true cost difference. This also demonstrates why daily compounding on credit cards (typically 19–21% nominally) feels even more expensive—the EAR can exceed 23%.
Future Value Calculations with EAR
Beyond interest rates, you can project investment or loan balances forward. If you deposit £5,000 into an account earning 8% annually, compounded quarterly, after 3 years you'll have:
Final Balance = Initial × (1 + r/m)^(m×t)
Plugging in: £5,000 × (1 + 0.08/4)^(4×3) = £5,000 × (1.02)^12 ≈ £6,347
For continuous compounding (rate r, time t years):
Final Balance = Initial × e^(r×t)
This formula is less common in retail banking but appears in academic finance and certain bond valuations.
Common Pitfalls When Using EAR
Understanding these practical traps helps you avoid costly financial decisions.
- Confusing nominal with effective rate — Banks legally disclose the nominal rate prominently, but that's not what you pay. Always convert to EAR when comparing products. A 0.1% difference in EAR can cost hundreds of pounds over a loan's lifetime on large amounts.
- Overlooking compounding frequency differences — Two loans at 10% look identical until you check compounding. One compounded monthly (EAR ≈ 10.47%) differs from one compounded annually (EAR = exactly 10%). On a £50,000 mortgage, this gap accumulates quickly.
- Assuming daily compounding is always worst — While daily compounding typically increases the effective rate, it's not automatic. A 7% loan compounded monthly (EAR ≈ 7.23%) may be pricier than 7.1% compounded annually (EAR = 7.1%). Always calculate, don't assume.
- Forgetting about fees and other costs — EAR only captures interest compounding. Origination fees, annual charges, or early repayment penalties aren't included in EAR calculations. Add these separately to assess the true financial cost.