# Annual Percentage Rate (APR) vs Effective Annual Rate (EAR): the differences

1. Annual Percentage Rate (APR)

• APR is the standard way to quote interest rate when banks lend money to borrowers and earn interest.
• APR is calculated on many consumer loans, mortgages and credit cards.
• APR is the nominal interest rate offered by the bank, and is not the actual interest rate.
• APR does not include the effects of intra-year compounding, where EAR does.
• APR is the standard cost of borrowing, often used when comparing lenders and loan options.
• APR is always lower than AER.
• APR creates an impression that customers can borrow money from banks relatively cheaply.

2. Effective Annual Rate (EAR)

• EAR is the standard way to quote interest rate, when banks pay interest to customers who deposit money with them.
• EAR is applicable to deposit accounts (savings accounts, CDs).
• EAR is the effective return assuming that interest paid is reinvested at the same rate.
• EAR includes the effects of intra-year compounding.
• EAR is used when comparing investments with different compounding periods per year.
• EAR is always higher than APR, and it increases with the number of compounding periods per year (C/Y). EAR equals to APR when there is no intra-year compounding,
• EAR creates an impression that customers can earn a higher interest by depositing the money in banks.

Formula:
EAR = (1+APR÷n)^n－1,
where n represents the number of compounding periods per year (typically n=12 months).
The result likely will be a slightly higher interest rate, since a 10% APR equates to a 10.47% EAR.

Example:
A bank offers Periodic Rates with 10% APR
1. APR:
Annual Percentage Rate: APR = 10%
Semi-Annual Rate (compounds twice a year)
10%÷2 = 5%
Monthly Rate (compounds twelve times a year)
10%÷12 = 0.833%
2. EAR:
Effective Annual Rates: EAR = (1+APR÷n)^n)－1,
Semi-Annual Rate (n=2) of 5%, EAR = (1 + 0.1÷2)^2－1 = 10.25%
Monthly Rate (n=12) of 0.833%, EAR = (1 + 0.1÷12)^12－1 = 10.47%

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