What is APR?
APR (Annual Percentage Rate) represents the yearly cost of a loan, including fees and interest, expressed as a percentage. It provides a standardized way to compare different loan offers.
Unlike the nominal interest rate, APR includes origination fees, closing costs, and other charges, giving you a more accurate picture of the total cost of borrowing.
What is APY?
APY (Annual Percentage Yield) shows the total interest earned on an investment over one year, taking into account compound interest.
While APR is typically used for loans, APY is often used for investments and savings accounts to show the effective annual return when interest is compounded multiple times per year.
Compounding Frequency
The frequency of compounding can significantly impact the effective interest rate:
- Monthly compounding: Interest is calculated and added to the principal 12 times per year
- Quarterly compounding: Interest is calculated 4 times per year
- Daily compounding: Interest is calculated every day
- Continuous compounding: Interest is calculated continuously, resulting in the highest effective rate
Higher compounding frequency results in higher effective interest rates.
Understanding Interest Rates
APR vs. APY: What's the Difference?
APR (Annual Percentage Rate)
- Does not account for compounding
- Used primarily for loans and credit cards
- Includes fees and other costs
- Shows the simple interest rate plus fees
APY (Annual Percentage Yield)
- Accounts for compounding interest
- Used primarily for savings and investments
- Shows the actual return over a year
- Always higher than the nominal rate (except for annual compounding)
How APR is Calculated
APR is calculated using this basic formula:
APR = ((Fees + Total Interest) / Principal / Loan Term in Years) × 100%
This formula takes into account both the interest rate and any additional fees charged on the loan, providing a more accurate representation of the total cost of borrowing.
How APY is Calculated
APY is calculated using this basic formula:
APY = (1 + r/n)^n - 1
Where:
- r = nominal annual interest rate (as a decimal)
- n = number of compounding periods per year
For continuous compounding, the formula becomes:
APY = e^r - 1
Where e is the mathematical constant approximately equal to 2.71828.
Why These Calculations Matter
For borrowers: Understanding APR helps you compare loan offers accurately and determine the true cost of borrowing.
For investors: Understanding APY helps you compare investment opportunities and calculate your actual returns taking compounding into account.
Common Compounding Frequencies
| Compounding Frequency | Times Per Year | Example APY (5% Nominal Rate) |
|---|---|---|
| Annually | 1 | 5.00% |
| Semi-annually | 2 | 5.06% |
| Quarterly | 4 | 5.09% |
| Monthly | 12 | 5.12% |
| Daily | 365 | 5.13% |
| Continuous | ∞ | 5.13% |
Frequently Asked Questions
What's the difference between interest rate and APR?
Interest rate is the percentage of the loan amount that the lender charges for borrowing money, while APR (Annual Percentage Rate) includes both the interest rate and additional fees associated with the loan, providing a more comprehensive view of the total cost of borrowing.
Why is APY always higher than the nominal interest rate?
APY (Annual Percentage Yield) is higher than the nominal rate because it takes into account the effect of compounding. When interest is compounded more frequently than once a year, the effective annual rate increases because interest earns interest within the year.
How do lenders use APR?
Lenders are required by law to disclose the APR to borrowers, allowing them to compare different loan offers more accurately. APR provides a standardized way to understand the true cost of borrowing beyond just the interest rate.
Why does compounding frequency matter?
The frequency of compounding affects how quickly interest accumulates. More frequent compounding results in a higher effective annual rate because interest is calculated and added to the principal more often, creating a compounding effect where interest earns interest.
Can APR and APY be the same?
APR and APY can be the same only when interest is compounded exactly once per year (annual compounding). In all other cases where compounding occurs more frequently, APY will be higher than APR.