Effective interest rate

Effective interest rate

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Effective interest rate

The effective interest rate, effective annual interest rate, Annual Equivalent Rate (AER) or simply effective rate is the interest rate on a loan or financial product restated from the nominal interest rate as an interest rate with annual compound interest.^[1] It is used to make loans with different compounding terms (daily, monthly, annually, or other) more comparable.

The effective interest rate differs in two important respects from annual percentage rate: first, the effective interest rate generally does not incorporate one-time charges such as front-end fees or other "unusual" features; second, the effective interest rate is (generally) not a term defined by legal or regulatory authorities (as annual percentage rate is in many jurisdictions).

Annual Percentage Yield or effective annual yield is the analogous concept used for savings or investment products, such as a certificate of deposit. Since any loan is an investment product for the lender, the terms may be used to apply to the same transaction, depending on the point of view.

It is important to note that effective annual interest or yield may be calculated or applied differently depending on the circumstances, and the definition should be studied carefully. For example, a bank may refer to the yield on a loan portfolio after expected losses as its effective yield and include income from other fees, meaning that the interest paid by each borrower may differ substantially from the bank's effective yield.

Calculation

The effective interest rate is calculated as if compounded annually. The effective rate is calculated in the following way, where r is the effective annual rate, i the nominal rate, and n the number of compounding periods per year (for example, 12 for monthly compounding):

r \ = \ (1+i/n)^{n} - 1

For example, a nominal interest rate of 6% compounded monthly is equivalent to an effective interest rate of 6.17%. 6% monthly is credited as 6%/12 = 0.5% every month. After one year, the initial capital is increased by the factor (1+0.005)¹² ≈ 1.0617. (n.b.: Percentage figures must always be divided by 100, as the percent sign is a notation convenience; e.g. 6% = 0.06).

When the frequency of compounding is increased up to infinity the calculation will be:

r \ = \ e^i - 1

The yield depends on the frequency of compounding.

Effective Annual Rate Based on Frequency of Compounding
Nominal Rate	Semi-Annual	Quarterly	Monthly	Daily	Continuous
1%	1.002%	1.004%	1.005%	1.005%	1.005%
5%	5.062%	5.095%	5.116%	5.127%	5.127%
10%	10.250%	10.381%	10.471%	10.516%	10.517%
15%	15.563%	15.865%	16.075%	16.180%	16.183%
20%	21.000%	21.551%	21.939%	22.134%	22.140%
30%	32.250%	33.547%	34.489%	34.969%	34.986%
40%	44.000%	46.410%	48.213%	49.150%	49.182%
50%	56.250%	60.181%	63.209%	64.816%	64.872%