Effective Annual Rate Calculator
What is Effective Annual Rate (EAR)?
The Effective Annual Rate (EAR), also known as the Annual Equivalent Rate (AER) or Annual Percentage Yield (APY), is the actual interest rate an investment earns or a loan costs after accounting for the effects of compounding. While the nominal interest rate (the stated rate) assumes interest is calculated only once per year, the EAR reveals the true financial impact when interest is compounded more frequently (e.g., monthly, quarterly, or daily).
In simple terms, EAR answers the question: "If I started with $100 and let it grow for a year with compounding, what percentage of profit would I actually have at the end?"
The EAR Formula
The standard formula used to calculate the Effective Annual Rate varies slightly depending on whether the compounding is discrete or continuous.
Discrete Compounding Formula
For standard compounding periods (monthly, daily, etc.):
- i = The nominal annual interest rate (as a decimal, e.g., 0.05 for 5%).
- n = The number of compounding periods per year.
Continuous Compounding Formula
For continuous compounding, which assumes interest is calculated at every possible instant:
- e = Euler's number (mathematical constant approx. 2.71828).
- i = The nominal annual interest rate.
Why is EAR Important?
Understanding the difference between the nominal rate and the effective rate is crucial for both borrowers and investors:
- For Investors/Savers: EAR allows you to compare savings accounts with different compounding frequencies. A 5% rate compounded daily yields more than a 5% rate compounded annually.
- For Borrowers: Lenders often advertise the nominal rate (or APR) because it looks lower. The EAR shows the true cost of the debt if interest accumulates on top of interest.
Example Calculation
Let's assume you are comparing two investment options:
- Option A: 10% nominal interest compounded annually.
- Option B: 9.8% nominal interest compounded monthly.
Option A EAR: Since it compounds annually, the EAR is exactly 10.00%.
Option B EAR: Using the formula: (1 + 0.098 / 12)12 – 1 = 10.25%.
Even though Option B has a lower "sticker price" rate (9.8% vs 10%), it is actually the better investment because the monthly compounding results in a higher effective yield.
How Compounding Frequency Affects Returns
The more frequently interest is compounded, the higher the effective rate becomes relative to the nominal rate. However, the returns diminish marginally as frequency increases. The jump from annual to semi-annual is significant, while the jump from daily to continuous is negligible for most amounts.