Effective Annual Rate (EAR) or Effective Interest Rate (EIR)
Effective APR, also known as the effective annual rate (EAR) or effective interest rate (EIR), differs from nominal APR because it takes into account the effects of compounding interest.
Compounding occurs when interest is charged on both the initial principal and any accumulated interest. This distinction is important because the more frequently interest is compounded (daily, monthly, quarterly, etc.), the higher the overall cost of borrowing.
Key differences between APR and effective APR:
APR (Nominal APR)
Reflects the simple annual cost of borrowing, not accounting for compounding.
It includes the base interest rate and any additional fees, but doesn’t factor in how often interest is applied (compounded) within a year.
APR is typically lower than the effective APR.
Effective APR (EAR)
Takes into account how often interest is compounded during the year.
Provides a more accurate reflection of the total cost or return because it factors in the effect of interest compounding over time.
The more frequently the interest is compounded, the higher the effective APR will be compared to the nominal APR.
Formula:
Effective APR = (1 + (APR ÷ 𝑛))^𝑛 − 1
Where:
APR is the nominal APR (annual percentage rate)
n is the number of compounding periods in a year (e.g., 12 for monthly compounding)
Example
Suppose you have a loan with an APR of 10% that compounds monthly (12 times per year).
Using the formula:
Effective APR = (1 + (0.10 ÷ 12))^12 − 1 = 10.47%
The effective APR (10.47%) is slightly higher than the nominal APR (10%) due to monthly compounding.
Financial Glossary
Use Lighter Capital's glossary to understand common terms used in finance and investing, so you can build financial literacy and make informed decisions for your startup.
Effective Annual Rate (EAR) or Effective Interest Rate (EIR)
Effective APR, also known as the effective annual rate (EAR) or effective interest rate (EIR), differs from nominal APR because it takes into account the effects of compounding interest.
Compounding occurs when interest is charged on both the initial principal and any accumulated interest. This distinction is important because the more frequently interest is compounded (daily, monthly, quarterly, etc.), the higher the overall cost of borrowing.
Key differences between APR and effective APR:
APR (Nominal APR)
Reflects the simple annual cost of borrowing, not accounting for compounding.
It includes the base interest rate and any additional fees, but doesn’t factor in how often interest is applied (compounded) within a year.
APR is typically lower than the effective APR.
Effective APR (EAR)
Takes into account how often interest is compounded during the year.
Provides a more accurate reflection of the total cost or return because it factors in the effect of interest compounding over time.
The more frequently the interest is compounded, the higher the effective APR will be compared to the nominal APR.
Formula:
Effective APR = (1 + (APR ÷ 𝑛))^𝑛 − 1
Where:
APR is the nominal APR (annual percentage rate)
n is the number of compounding periods in a year (e.g., 12 for monthly compounding)
Example
Suppose you have a loan with an APR of 10% that compounds monthly (12 times per year).
Using the formula:
Effective APR = (1 + (0.10 ÷ 12))^12 − 1 = 10.47%
The effective APR (10.47%) is slightly higher than the nominal APR (10%) due to monthly compounding.
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