Being able to convert interest rates over different periods of time is important in order to make sure you’re getting the best deal on your loan or the highest interest rate for your savings. For example, one loan offer might state a monthly interest rate, while another might state the interest rate as an annual rate. In addition, you need to know whether the annual interest rate is stated as an annual percentage rate or as an annual percentage yield.
Simple vs. Compound Interest
The more often interest compounds, the higher the effective annual interest rate. This is because each time the interest compounds, the interest that has accrued to that point is added to the account balance and begins to accrue additional interest. For example, if interest compounds monthly, after the first month the accrued interest is added to the balance and then earns additional interest over the next 11 months of the year.
Simple Interest Rate Conversion
If the annual interest rate you start with is the nominal interest rate, which means that it is the sum of the monthly rates, then it’s a simple calculation. Divide the annual interest rate by 12 to find the monthly interest rate. For example, if a bank quotes you a 6 percent annual percentage rate, divide 6 by 12 to find that the monthly interest rate is 0.5 percent.
Compound Interest Rate Conversion
If the annual interest rate you start with is the effective interest rate, meaning it already includes the impact of interest being compounded each month throughout the year, then the formula gets more complicated. You'll need to follow these steps:
- Convert the interest rate as a percentage to a decimal by dividing by 100.
- Add 1 to the interest rate as a decimal.
- Raise the result to the 1/12th power because there are 12 months per year.
- Subtract 1 from the result to find the monthly interest rate as a decimal.
- Multiply by 100 to find the monthly interest rate as a percentage.
For example, if instead of a 6 percent annual percentage rate the bank quotes a 6 percent annual percentage yield, then first divide by 100 to get 0.06. Second, add 1 to 0.06 to get 1.06. Third, raise 1.06 to the 1/12th power to get 1.004867551. Fourth, subtract 1 to find that the monthly interest rate as a decimal is 0.004867551. Fifth, multiply 0.004867551 by 100 to find that the monthly interest rate equals 0.4867551.
- This computation is exactly the same for computing weekly or daily interest. Just divide the APR by the number of time units in a year. For instance, 52 for weekly interest rate or 365 for the daily rate.