Annual Percentage Rate (APR) Calculation: A Comprehensive Guide

When you're taking out a loan, you want to make sure you're getting the lowest interest rate possible. Or, if you're going to be earning interest, you want to make sure you get the highest rate. However, interest rates may be listed using a different time period than annually such as 0.75 percent per month or 1.6 percent per quarter. To compare those rates, you need to convert them to an annual rate. You'll also need to know how interest is compounded on the account. If interest is only added to the balance once per year, you can use the simple interest formula. However, if interest compounds each period, meaning it's added to the balance at the end of each period, you'll need to use the compound interest formula.

How to Calculate Interest Rate Per Annum

Simple Interest Formula

To convert the periodic interest rate to an annual interest rate using the simple interest formula, simply multiply the periodic interest rate by the number of periods per year to calculate the interest rate per annum. For example, if the interest rate is 0.75 percent per month, there are 12 months per year. So, multiply 0.75 percent by 12 to find that the interest rate per annum equals 9 percent. Or, if the interest rate is 1.6 percent per quarter, there are four quarters per year. So, multiply 1.6 percent by four to find the annual interest rate is 6.4 percent.

Compound Interest Formula

The compound interest formula is more complicated because it takes into account the impact of interest compounding, which refers to the fact that when interest is added to the account after each period, that interest incurs additional interest for the rest of the year.

To convert a periodic rate to an annual compound interest rate, convert the periodic interest rate to a decimal. Then, add 1. Next, raise the result to the power of the number of periods per year. Then, subtract 1. Finally, multiply by 100.

For example, with a 0.75 percent interest rate compounded monthly, divide 0.75 percent by 100 to get 0.0075. Then, add 1 to get 1.0075. Next, because there are 12 months per year, raise 1.0075 to the 12th power and get 1.0938. Then, subtract 1 to get 0.0938. Finally, multiply by 100 to find that the interest rate per annum is 9.38 percent.

For a quarterly rate, the steps are the same, but in the third step, you raise the result to the fourth power because there are four quarters per year. For example, take a 1.6 percent quarterly rate. Divide by 100 to get 0.016. Then, add 1 to get 1.016. Next, raise 1.016 to the fourth power to get 1.0656. Then, subtract 1 to get 0.0656. Finally, multiply by 100 to find the annual compound interest rate is 6.56 percent.