What Is the Effective Annual Rate (EAR)?
Even for the same 'annual 6%,' the interest you end up holding differs depending on whether it's applied once a year or every month. What sorts out this difference is the effective annual rate (EAR).
Nominal rate and effective annual rate
The nominal rate (annual rate) is the surface rate shown as just 'annual 6%.' But depending on how many times interest is applied per year (the compounding frequency), how much it actually grows differs.
The effective annual rate (EAR) is the 'true annual rate' that reflects all the compounding effects. The formula is EAR = (1 + nominal rate ÷ n)^n - 1, where n is the number of times compounded per year.
The difference the compounding frequency makes
Let's take annual 6% as an example.
(1) Once a year (annual compounding): EAR = 6.00%.
(2) Monthly (monthly compounding): (1 + 0.06/12)^12 - 1 ≈ 6.17%.
(3) Daily (daily compounding): about 6.18%.
The more compounding periods, the slightly larger the EAR. Applied infinitely often (continuous compounding), it converges to e^0.06 - 1 ≈ 6.18%. The higher the interest rate, the wider this gap grows.
When comparing deposits or loans, you should compare on the basis of the effective annual rate (or an effectively identical concept) rather than the nominal rate, to be fair.
Why you need to know the EAR
Each financial product has a different interest-calculation cycle. If one deposit is annual 6% compounded annually and another is annual 5.9% compounded monthly, it's hard to tell from the surface numbers which is more favorable. Converting to EAR lets you compare apples to apples.
It's the same with loans. Even if the surface rate looks low, the effective burden reflecting the compounding cycle and fees can be higher. It's important to have a sense that the 'stated rate' and the 'rate that actually stays in or leaves your hands' are different.
Frequently Asked Questions
Q. Is more frequent compounding always to my advantage?
For a deposit (the receiving side), the more frequent the compounding, the higher the effective rate, so it's favorable. Conversely, for a loan (the paying side), the more frequent the compounding, the greater the effective burden. That said, the difference is not large when the rate is low.
Q. Are the effective annual rate and CAGR related?
Closely. They are cousins in that both are 'the actual compound result converted to an annual rate.' You can think of EAR as dealing with the compounding-frequency issue of an interest rate, and CAGR with the compound conversion of actual investment performance.
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